Question

How do you find the inverse of `f(x)=2x+3`?

Answer 1

`g(x)=(x-3)/2` is the inverse of `f(x)=2x+3`

Explanation:

If `f(x) = 2x+3`
then for any function `g(x)`
`color(white)("XX")f(g(x)) = 2(g(x))+3`

If `g(x)` is the inverse of `f(x)`
`color(white)("XX")f(g(x)) = x`

Therefore, if `g(x)` is the inverse of `f(x)`
`color(white)("XX")2g(x)+3 =x`

`color(white)("XX")rarr 2g(x) = x-3`

`color(white)("XX")rarr g(x) = (x-3)/2`

Note that your instructor may have some special form they want you to use for the inverse of `f(x)`; for example `bar(f(x))` or `f^(-1)(x)`; if so replace `g(x)` with whatever form your instructor desires.