Find functions f and g so that f ∘ g = H.
-H(x)= ∣
A)f(x)= ∣ ; g(x)= 8x + 8
B)f(x)= g(x)= 8x + 8
C)f(x)= g(x)= 8x - 8
D)f(x)= x; g(x)= 8x + 8

Question

Find functions f and g so that f ∘ g = H.
-H(x)= ∣ 
A)f(x)= ∣ ; g(x)= 8x + 8 
B)f(x)= g(x)= 8x + 8 
C)f(x)= g(x)= 8x - 8 
D)f(x)= x; g(x)= 8x + 8

Quizplus · Accepted Answer

To find the functions f and g that satisfy f ∘ g = H, we need to consider the inputs and outputs of each function.

Looking at the expression for H(x), we can see that it involves a long string of characters and numbers. This suggests that the function H(x) is not something that we can easily decompose into simpler functions. Instead, we need to look for functions f and g that can recreate this expression when composed together.

One approach is to notice that the string of characters and numbers in H(x) contains some repeated patterns, such as "11ebbed0_ca9a_5903_8acb_" and "_TB8253_11". This suggests that we might be able to construct f and g by combining smaller functions that generate these patterns.

In option A, the function g(x) = 8x + 8 is a simple linear function that adds a constant value to the input x. This suggests that g(x) might be useful for generating the pattern "_TB8253_11", since adding a constant value to each input will not change this pattern.

The function f(x) = ∣11ebbed0_ca9a_5904_8acb_7d4f026e931c_TB8253_11| is a bit more complicated, since it involves taking the absolute value of a long string of characters and numbers. However, we can see that this string of characters and numbers matches the first part of the pattern in H(x): "11ebbed0_ca9a_5903_8acb_". This suggests that f(x) might be useful for generating this part of the pattern.

If we compose f and g together, we get:

(f ∘ g)(x) = f(g(x)) = f(8x + 8) = ∣11ebbed0_ca9a_5904_8acb_7d4f026e931c_TB8253_11|

This expression is exactly equal to H(x), so we have found the functions f and g that satisfy the condition f ∘ g = H.

Option B cannot be correct because the function f is different in that option. Option C cannot be correct because the function f is different in that option. Option D cannot be correct because the function f is not defined to be the same as H(x) in that option.

Find Functions F and G So That F ∘ G