Inverses Using Function Composition

When using composition to verify 2 functions are inverses, g(f(x)) and f(g(x)) must equal

The inverse of the function f(x) is written as ...

What are the missing values if g(x)=f^-1(x)?

Verify if the functions are inverses using composition of functions:

Solve the equation involving the inverse function: $$f^{-1}(f(x)) = 12$$ .

Are the following inverses of each other? Use composition of functions. fog(x) and gof(x)

If $$f(x) = x^2$$ and $$g(x) = \sqrt{x}$$ , are $$f\left(x\right)$$ and $$g\left(x\right)$$ inverse functions?

Are these functions inverses of each other?

$$h\left(x\right)=-\frac{1}{3}x+\frac{1}{3}$$

$$f\left(x\right)=-3x+1$$

What is the composition of a function and its inverse, $$f(f^{-1}(x))$$ ?

The algebraic process used to formally prove that two functions are inverses is called: