Verify that f(x) and g(x) are inverse functions: f(x)=3x^3+5, g(x)=3x-5

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Step-by-step explanation:

The question says:

And it says to verify that both functions are inverses of each other.

To show this, we have to understand one composition of function property. When 2 functions are inverses of each other, the composition of both functions should yield "x". In notation:

(f o g)(x) = f(g(x)) = x

and

(g o f)(x) = g(f(x)) = x

So, we need to show that putting f(x) into g(x) and putting g(x) into f(x) both yields "x". Lets show this:

First:

Verified.

Second:

Verified.

We have shown that both the functions are inverse of each other.

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.