Question

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1->
Inverse
Functions
5
f(x)=√x-8 and g(x)=x5 +8
Part 1 of 3
Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are in
each other.
f(g(x)) =
O Points:
0 of 1

Answer 1

To find f(g(x)) and g(f(x)), we need to substitute the function expressions into each other.

1. To find f(g(x)):

Substitute g(x) into f(x):

f(g(x)) = f(x^5 + 8)

2. To find g(f(x)):

Substitute f(x) into g(x):

g(f(x)) = g(√x - 8)

Now, let's determine whether the pair of functions f and g are inverses of each other.

For f(g(x)) to be equal to x and g(f(x)) to be equal to x, the following conditions must be met:

1. f(g(x)) = x

2. g(f(x)) = x

To determine if f(g(x)) = x, substitute the expression for f(g(x)):

f(g(x)) = f(x^5 + 8)

= √(x^5 + 8) - 8

To determine if g(f(x)) = x, substitute the expression for g(f(x)):

g(f(x)) = g(√x - 8)

= (√x - 8)^5 + 8

Comparing these expressions with x, we can see that neither f(g(x)) nor g(f(x)) are equal to x. Therefore, the pair of functions f and g are not inverses of each other.

I hope this helps!

Explanation: