Question

Which function is the inverse of ſx) - 2x+ 3?

Answer 1

If $f^{-1}(x)$ is the inverse of $f(x)$, then

$f\left(f^{-1}(x)\right) = x$

which means

$2f^{-1}(x)+3 = x$

Solve for $f^{-1}(x)$ :

$2f^{-1}(x) + 3 = x \\\\ 2f^{-1}(x) = x - 3 \\\\ f^{-1}(x) = \dfrac{x-3}2 = \boxed{\dfrac12x-\dfrac32}$