Question

F(x)= (x+1)/2

g(x)= 2x-1

Show your work to prove that the inverse of f(x) is g(x).

Show your work to evaluate g(f(x)).

Please help! I don't understand how to prove that they're inverse of eachother.

Answer 1

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Answer:

g(f(x)) = x . . . so the functions are inverses

Explanation:

Two functions f and g are inverses of each other if ...

g(f(x)) = x or f(g(x)) = x

We are asked to evaluate g(f(x)). That will be x if the functions are inverses.

g(f(x)) = g((x+1)/2) = 2((x +1)/2) -1 = (x +1) -1

g(f(x)) = x . . . . the functions are inverses