f(x)=1/4x+5 G(x)=4x-20

Answer 1

One way to find whether these are inverses is to see if f(g(x)) = x.

Let's test this:

g(x) = 4x - 20

f(g(x)) means that everywhere we see x in f(x) we plug in g(x) which is 4x - 20.

f(g(x)) = 1/4 * (4x - 20) + 5 = (x - 5) +5 = x, so yes f(x) and g(x) are inverses of each other.

Another way to test this is:

1) f(x) = 1/4x + 5 or y = 1/4x + 5

2) Switch x and y in the expression: x = 1/4y + 5

3) Solve for y: x = 1/4y + 5 -> x - 5 = 1/4y -> y = 4(x - 5) -> y = 4x - 20

4) Therefore the inverse of f(x) is g(x) = 4x - 20.