Determine whether the given functions are inverses of each other.
-f(x) = 4x,
A) Yes
B) No

Question

Determine whether the given functions are inverses of each other.
-f(x) = 4x, 
A) Yes 
B) No

Quizplus · Accepted Answer

We need to find out if f(g(x))=x and g(f(x))=x for all values of x.

f(g(x))=f((x-1)/3)
=4((x-1)/3)
=(4x-4)/3

Now we need to simplify this expression to see if it is equal to x.

(4x-4)/3=(3(4x-4))/9
=(12x-12)/9
=4(x-1/3)

Therefore, f(g(x))=4(x-1/3). We notice that this is just f(x) with x replaced with (x-1)/3. Therefore, f(g(x))=x is true for all values of x.

Now we need to test g(f(x))=x.

g(f(x))=((4x)/3)+1
= (4x+3)/3

We need to simplify this expression to see if it is equal to x.

(4x+3)/3= (3(4x+3)-9)/9
=(12x+9-9)/9
=12x/9
=4x/3

Therefore, we notice that g(f(x)) is just g(x) with x replaced with (4x/3)+1. Therefore, g(f(x))=x for all values of x.

Since f(g(x))=x and g(f(x))=x for all values of x, f(x) and g(x) are inverses of each other.

Determine Whether the Given Functions Are Inverses of Each Other