Question

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

Answer 1

`color(green)(1/2)`

Explanation:

If `f(x)=2x+3`
and `g(x)` is the inverse of `f(x)`
then
`color(white)("XXX")f(g(x))=x`

`color(white)("XXX")rarr 2g(x)+3=x`

`color(white)("XXX")rarr g(x)=1/2x-3/2`

and using the power rule for derivatives:
`color(white)("XXX")(g(x))/(dx) = 1/2`