Question

Given f(x) = 3x +1 and (f o g)(x) = 6 - 1/2x, how do you find the function g?

Answer 1

`g(x)=5/3-1/6x`

Explanation:

`f(x)=3x+1`
`(f@g)(x)=6-1/2x`
'~~~~~~~~~~~~~~~~~~~~~~~~~
`=>3[g(x)]+1=6-1/2x`

`3[g(x)]=5-1/2x" "larr" subtract 1 from both sides"`

`g(x)=5/3-1/6x" "larr" divide both sides by 3"`