Question

HELP ASAP!!

f(x) = 1/3 x + 2

- find the inverse of f(x) and name it g(x). show and explain your work.
- use function composition to show that f(x) and g(x) are inverses of each other.

Answer 1

replace f(x) with y
switch x and y
solve for y
replace y with g(x)

y=1/3x+2
x=1/3y+2
x-2=1/3y
3x-6=y
g(x)=3x-6

f(g(x)) should have the same result as g(f(x)) which should be x

f(g(x))=1/3(3x-6)+2=x-2+2=x
g(f(x))=3(1/3x+2)-6=x+6-6=x

the inverse is g(x)=3x-6