Question

Q. 23 : If f is an invertible function defined as f(x) = 3x-45, then f^(x) is​

Answer 1

$\bold{let,f(x)=y= \frac{3x - 4}{5}}$

$\bold{So, to \: find \: inverse \: of  \: f(x) we }$

$\bold{need x in \: terms \: of \:  y  \: which \: is \: {f}^{ - 1} (x)}$

$\bold{\therefore{y= \frac{3x - 4}{5}} }$

⇒5y=3x−4

⇒5y+4=3x

$\bold{\implies \bold{{(x)= \frac{5y + 4}{3}} }}$

$\bold{\therefore {f}^{ - 1} \bold{{(y)= \frac{5y + 4}{3}} }}$

${ \bold{\therefore {f}^{ - 1} \bold{{(x)= \frac{5x + 4}{3}} }}{  \bold{(replacing \:  y \:  with  \: x}}})$