Question

Let f : R -$\left\{\frac{-3}{5}\right\}\to R$ be a function defined by f(x) = $\frac{2x}{5x+3}$ find $f^{-1}$ (x)

Answer 1

It is given that

$f:R-\{-3/5\}\to R$

and, $f\left(x\right)=\frac{2x}{5x+3}$

Let $f\left(x\right)=y$. Then,

$f\left(x\right)=y\Rightarrow \frac{2x}{5x+3}=y$

$\Rightarrow 2x-5xy=3y$

$\Rightarrow x(2-5y)=3y$

$\Rightarrow x=3y$

$(2-5y)$

Thus, $f^{-1}$ is given by $f^{-1}\left(x\right)=\frac{3x}{(2-5x)}$, forall $x\in R-\left\{\frac{2}{5}\right\}$