Verify that f and g are inverse functions. Find f(g(x)) and g(f(x))

Question

1: f(x)=x+2; g(x)=x-2

2: f(x)= 4x-1; g(x)=1/4x+1/4

please help.

Answer 1

You can verify that functions are inverses by taking f(g(x)) and by taking g(f(x)). If they both equal "x" then the functions are inverses.

For f(x) = x + 2 and g(x) = x - 2:

Then f(g(x)) = f(x - 2) = (x - 2) + 2 = x

And g(f(x)) = g(x + 2) = (x + 2) - 2 = x

Therefore f(x) and g(x) are inverse functions

For f(x) = 4x - 1 and g(x) = (1/4)x + 1/4:

Then f(g(x)) = f((1/4)x + 1/4) = 4((1/4)x + 1/4) - 1 = x + 1 - 1 = x

And g(f(x)) = g(4x - 1) = (1/4)(4x - 1) + 1/4 = x - 1/4 + 1/4 = x

Therefore f(x) and g(x) are inverse functions

Answer 2

To find the inverse of a function expressed as y=f(x), interchange the roles of x and y and solve for y.

For example y=x+2 -> interchange x=y+2 and y=x-2...so the answer to the first one is "yes".

You do the other one.