Question

If $f: R \rightarrow R$ defined by $f(x)=\frac{3 x+5}{2}$ is an invertible function, find $f^{-1}$.

Answer 1

SOLUTION : Let $f(x)=y \quad \therefore \quad y=\frac{3 x+5}{2}$

Since $f(x)$ is invertible

$\therefore \quad 3 x+5=2 y \quad \Rightarrow \quad 3 x=2 y-5 \quad \Rightarrow \quad f^{-1}(y)=\frac{2 y-5}{3} \text { Hence } f^{-1}(x)=\frac{2 x-5}{3} \\$