Question

If f(x)= 5x+3 and gof(x) =12x-5 ,find the inverse of the function g(x)

Answer 1

First, let us determine the function $g$. We know that $f(x) = 5x+3, \;\; g(f(x)) = 12x-5$ . Therefore, $x = \dfrac{f(x)-3}{5}$ and $g(f(x)) = 12\cdot\dfrac{f(x)-3}{5}-5 = 2.4f(x) -12.2.$ So $g(x) = 2.4x-12.2, \;\; x = \dfrac{g(x)+12.2}{2.4}$

The inverse $g^{-1}(g(x)) = x,$ and $g^{-1}(y) = \dfrac{y+12.2}{2.4}$ .