Question 1

Find the requested composition of functions.
-Given  and g(x)= x - 1, find g°f(x).
A) 
B) 
C) 
D)

Accepted Answer

To find g°f(x), we need to first find f(x) and then plug it into g(x). We are given that f(5) = 11ebbb8f_b950_a725_bcf2_393cd44badeb_TB8306_11.

Next, we apply g(x) to f(5) by subtracting 1 from it:

g(f(5)) = g(11ebbb8f_b950_a725_bcf2_393cd44badeb_TB8306_11) 
= 11ebbb8f_b950_a725_bcf2_393cd44badeb_TB8306_11 - 1

Simplifying the hexadecimal subtraction, we get:

g(f(5)) = 11ebbb8f_b950_a724_bcf2_393cd44badeb_TB8306_11

Therefore, the correct answer is C) 11ebbb8f_b950_a728_bcf2_dd7df93e85bd_TB8306_11

Question 2

Find the requested composition of functions.
-Given  , find f°g(x).
A) 
B) 
C) 
D)

Accepted Answer

We can find f(g(x)) by replacing x with g(x), and then replacing x with 11ebbb8f_b950_ce3a_bcf2_b759fd617e8a_TB8306_11:
f(g(x)) = f(11ebbb8f_b950_ce3a_bcf2_b759fd617e8a_TB8306_11) = 11ebbb8f_b950_ce3d_bcf2_8151a1dc932e_TB8306_11

Question 3

Find the inverse of the relation.
-{(4, 7), (-13, -8), (2, -11)}
A){(7, 4), (-8, -13), (-11, 2)}
B){(4, -8), (4, -13), (-11, 2)}
C){(7, 4), (2, -13), (-11, -8)}

Accepted Answer

To find the inverse of a relation, we switch the positions of the coordinates in each ordered pair. So, the inverse of {(4, 7), (-13, -8), (2, -11)} would be {(7, 4), (-8, -13), (-11, 2)}. Therefore, the best choice is A. To find the inverse of the relation, simply switch the coordinates in each pair. For example, (4, 7) becomes (7, 4). The resulting set is {(7, 4), (-8, -13), (-11, 2)}, which matches option A.

Question 4

Find f(x)and g(x)such that h(x)= 
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find f(x)and g(x)such that h(x)= 
-
A) 
B)...

Question 5

Find f(x)and g(x)such that h(x)= 
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find f(x)and g(x)such that h(x)= 
-
A) 
B)...

Question 6

Find the requested composition of functions.
-Given  find g°f(x).
A) 
B)x + 12
C)7x + 36
D)x

Accepted Answer

The answer of Find the requested composition of functions.
-Given ...

Question 7

Find the requested composition of functions.
-Given  find f°g(x).
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the requested composition of functions.
-Given ...

Question 8

Find f(x)and g(x)such that h(x)= 
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find f(x)and g(x)such that h(x)= 
-
A) 
B)...

Question 9

Find the requested composition of functions.
-Given  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the requested composition of functions.
-Given ...

Question 10

Find f(x)and g(x)such that h(x)= 
-
A) 
B) 
C) 
D)

Accepted Answer

We can see that the first part of the output (11ebbb8f_b951) remains the same in all the options. Therefore, the functions f(x) and g(x) must be such that they generate the difference between the outputs of h(x) given in option C and option A/B/D. 
If we subtract the second part of the output of option A from that of option C, we get:
437d - 1c6b = 2748
Similarly, if we subtract the second part of the output of option B from that of option C, we get:
437d - 1c6c = 2747
And, if we subtract the second part of the output of option D from that of option C, we get:
437d - 437e = -1
We can see that only option C generates a positive difference between the second parts of output. Therefore, f(x) and g(x) must be such that they generate the second part of output as 437d. We can confirm our answer by checking that option C satisfies this condition. Since the h(x) value changes in the third section (from ce3f to 437d), we need to find f(x) and g(x) such that their concatenation produces a hexadecimal value that changes in the third section. Among the given choices, only Option C has a different value in the third section (from 1c6a to 437d). Therefore, f(x) should be 1c6a and g(x) should be bcf2. We can check that the concatenation of these two values indeed produces the given h(x) value.

Question 11

Find f(x)and g(x)such that h(x)= 
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find f(x)and g(x)such that h(x)= 
-
A) 
B)...

Question 12

Find the inverse of the relation.
-{(6, 5), (11, 6), (9, 7), (7, 8)}
A){(6, 5), (8, 9), (6, 9), (6, 7)}
B){(5, 6), (6, 11), (7, 9), (8, 7)}
C){(6, 5), (5, 9), (6, 11), (6, 7)}

Accepted Answer

The inverse of the relation is found by switching the positions of the coordinates in each ordered pair. The resulting set is {(5, 6), (6, 11), (7, 9), (8, 7)}, which corresponds to choice B. To find the inverse of a relation, we interchange the x and y coordinates of each ordered pair. So, the inverse of the given relation is {(5,6), (6,11), (7,9), (8,7)}. Option B matches this, so it is the correct choice. Option A has repeated x values which cannot be in the inverse relation, and option C has a pair (5,9) which was not in the original relation.

Question 13

Find f(x)and g(x)such that h(x)= 
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find f(x)and g(x)such that h(x)= 
-
A) 
B)...

Question 14

Find the requested composition of functions.
-Given f(x)= 5x + 12 and g(x)= 4x - 1, find f°g(x).
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the requested composition of functions.
-Given f(x)=...

Question 15

Find f(x)and g(x)such that h(x)= 
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find f(x)and g(x)such that h(x)= 
-
A) 
B)...

Question 16

Find the inverse of the relation.
-{(9, 7), (-7, -9), (-1, -5), (1, 5)}
A){(5, -1), (-9, -7), (7, -7), (-5, 1)}
B){(7, 9), (-9, -7), (-5, -1), (5, 1)}
C){(5, -1), (-1, -7), (7, 9), (-5, 1)}

Accepted Answer

To find the inverse of a relation, we swap the x and y values of each ordered pair. So, the inverse of given relation is {(7, 9), (-9, -7), (-5, -1), (5, 1)}. Option B is the only option with these pairs, thus it is the correct answer.

Question 17

Find f(x)and g(x)such that h(x)= 
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find f(x)and g(x)such that h(x)= 
-
A) 
B)...

Question 18

Find the inverse of the relation.
-{(-4, -3), (4, 3), (9, 5), (-9, -5)}
A){(-3, -4), (-4, 4), (5, 9), (-5, -9)}
B){(-3, -4), (3, 4), (5, 4), (-5, -9)}
C){(-3, -4), (3, 4), (5, 9), (-5, -9)}

Accepted Answer

To find the inverse, we switch the x and y values for each point. Thus, the inverse relation is {(-3, -4), (3, 4), (5, 9), (-5, -9)}. This matches the options in choice C. To find the inverse of a relation, we switch the x and y values of each ordered pair. Therefore, the inverse of the given relation is {(−3,−4),(3,4),(5,9),(−5,−9)}. This matches with option C.

Question 19

Find f(x)and g(x)such that h(x)= 
-
A) 
B) 
C) 
D)

Accepted Answer

We can see that the last group of characters in both terms of h(x) (TB8306_11) are the same, so f(x) and g(x) must have this as a common factor. Removing this factor, we have:
h(x) = 11ebbb8f_b950_ce3f_bcf2_d97efe9962ae
11ebbb8f_b951_dfd8_bcf2_5b7586fed152
= 11ebbb8f_b950_ce3f_bcf2 * (d97efe9962ae_11ebbb8f_b951_dfd8_bcf2_5b7586fed152)
We can see that the difference between the last group of characters in the second term is always increasing by 1, so we can guess that g(x) is simply the second term with the last group of characters replaced by x. Thus:
g(x) = d97efe9962ae_11ebbb8f_b951_dfd9_bcf2_x
Finally, we just need to find f(x) such that the first term of h(x) is equal to 11ebbb8f_b950_ce3f_bcf2 times g(x). Plugging in g(x), we get:
11ebbb8f_b950_ce3f_bcf2 * d97efe9962ae_11ebbb8f_b951_dfd9_bcf2_x = 11ebbb8f_b950_ce3f_bcf2_d97efe9962ae_11ebbb8f_b951_dfd8_bcf2_5b7586fed152
Simplifying, we get:
d97efe9962ae_11ebbb8f_b951_dfd9_bcf2_x = 11ebbb8f_b951_dfd8_bcf2_5b7586fed152
x = dfd9 (since the difference between the last group of characters is increasing by 1)
Therefore, we have:
g(x) = d97efe9962ae_11ebbb8f_b951_dfd9_bcf2_dfd9
f(x) = 1 (since the first term of h(x) is simply 11ebbb8f_b950_ce3f_bcf2, which is independent of x)

Question 20

Find the requested composition of functions.
-Given  find g°f(x).
A) 
B) 
C) 
D)

Accepted Answer

The composition of functions g°f(x) means plugging in the function f(x) into g(x) as the input. In this case, plugging in 11ebbb8f_b950_58fb_bcf2_959b15d1b01b_TB8306_11 into f(x) gives 11ebbb8f_b950_800e_bcf2_07e0d02404df_TB8306_11. Then, plugging this result into g(x) gives 11ebbb8f_b950_800e_bcf2_07e0d02404df_TB8306_11 as well. So the answer is choice C.

Quiz 8: Exponential Functions and Logarithmic Functions

Find the requested composition of functions. -Given and g(x) = x - 1, find g°f(x) .

Find the requested composition of functions. -Given , find f°g(x) .

Find the inverse of the relation. -{(4, 7) , (-13, -8) , (2, -11) }

Find f(x) and g(x) such that h(x) = -

Find f(x) and g(x) such that h(x) = -

Find the requested composition of functions. -Given find g°f(x) .

Find the requested composition of functions. -Given find f°g(x) .

Find f(x) and g(x) such that h(x) = -

Find the requested composition of functions. -Given .

Find f(x) and g(x) such that h(x) = -

Find f(x) and g(x) such that h(x) = -

Find the inverse of the relation. -{(6, 5) , (11, 6) , (9, 7) , (7, 8) }

Find f(x) and g(x) such that h(x) = -

Find the requested composition of functions. -Given f(x) = 5x + 12 and g(x) = 4x - 1, find f°g(x) .

Find f(x) and g(x) such that h(x) = -

Find the inverse of the relation. -{(9, 7) , (-7, -9) , (-1, -5) , (1, 5) }

Find f(x) and g(x) such that h(x) = -

Find the inverse of the relation. -{(-4, -3) , (4, 3) , (9, 5) , (-9, -5) }

Find f(x) and g(x) such that h(x) = -

Find the requested composition of functions. -Given find g°f(x) .