Question

Confirm that f and g are inverses by showing the Composition of Inverses Rule for both f(g(x)) and g(f(x)) algebraically:
f(x)=9x+3
g(x)= (x-3)/9

thank you!

Answer 1

if y = 9 x + 3
reversing x and y yields
x = (y-3)/9

the other route
if y = (x-3)/9
reversing yields
x = (y-3)/9
9x = y - 3
or
y = 9 x + 3 sure enough

Answer 2

f(g) = 9g+3 = 9(x-3)/9+3 = x-3+3 = x
g(f) = (f-3)/9 = (9x+3-3)/9 = 9x/9 = x

That is the way to show that f and g are inverses