Question

for the functions f(x) = 5x +50 and g(x) = 1/5x -10 evaluate both f(g(x)) and g(f(x)). Are these functions inverses?

do you put them into each other?

Answer 1

f(x) = 5x+50
g(x) = x/5 - 10

f(g(x)) = 5(x/5-10) + 50
= x - 50 + 50 = x

g(f(x) = (5x+50)/5 - 10
= x + 10 - 10 = x

Yup they are

check:
let f(x) = 5x+50 be written as
y = 5x+50
to form the inverse, interchange the x and y
x = 5y + 50
now solve this for y
5y = x - 50
y = x/5 - 10

I was right.