Question

Algebra 2 help? Writing function compositions and inverses!! WILL GIVE MEDAL

Answer 1

\[f(x)=\frac{ 1 }{ 2 }x+1\]
a) find the inverse of f(x) and name it g(x). Show and explain your work.
b) Use function composition to show that f(x) and g(x) are inverses of each other.

Answer 2

i just need help with B now.

Answer 3

@alprincenofl ^^

Answer 4

its best to do this using an example
let f(x) = 3x - 2
let y = 3x - 2
3x = y + 2
x = (y = 2)/3

f'(x) = ( x + 2)/3 = g(x)

if g(x) is an inverse of f(x) then f(gx)) = x

so lets find f(g(x))

this = 3 ( x + 2)/3 - 2 = x +2 -2 = x

this verifies that g(x) is the inverse of f(x)

Answer 5

how would I do it with the fraction though?? .-. that's where I'm confused