Question

if f(x) is invertible function ,find the inverse of f(x)=(3x-2)/5.

Answer 1

concept : - if y = f(x) is a invertible function then, f(y) shows the inverse of f(x) .
$f(x)=\frac{3x-2}{5}\\\\\\Let,f(x)=y\\\\y=\frac{3x-2}{5}\\\\y\times\:5=3x-2\\\\5y+2=3x\\\\\frac{5y+2}{3}=x\\\\x=\frac{5y+2}{3}\\\\f(y)=\frac{5y+2}{3}$
hence,
$f^{-1}(x)=\frac{5x+2}{3}$

Answer 2

Answer:

$f^{-1}(x)=\frac{5x+2}{3}$

Step-by-step explanation:

Given : $f(x)=\frac{3x-2}{5}$

To Find: inverse of f(x)

Solution:

$f(x)=\frac{3x-2}{5}$

let f(x)=y

So,  $y=\frac{3x-2}{5}$

Find the value of x

$\frac{5y+2}{3}=x$

Now replace x with y and y with x

$\frac{5x+2}{3}=y$

Thus $f^{-1}(x)=\frac{5x+2}{3}$

Hence the inverse is   $f^{-1}(x)=\frac{5x+2}{3}$