Question

Find the inverse of the function
f(x) = 7x-4/ x+3

A) This function is not one to one and therefore it has no inverse

B) f^-1 (x) = -3x - 4 / x - 7

C) f^-1 (x) = x + 3 / 7x - 4

D) f^-1 (x) = 3x + 4 / x+7

Answer 1

we are given

function as

$f(x)=\frac{7x-4}{x+3}  $

step-1: Set f(x)=y

$y=\frac{7x-4}{x+3}  $

step-2: Switch x and y

$x=\frac{7y-4}{y+3}  $

step-3: Solve for y

now, we can solve for y

$x(y+3)=7y-4  $

$xy+3x=7y-4  $

$xy=7y-4-3x  $

$xy-7y=-4-3x  $

$y(x-7)=-4-3x  $

$y=\frac{-4-3x}{x-7}  $

so, we get

$f^{-1}(x)=\frac{-3x-4}{x-7}  $...............Answer

Answer 2

Answer:

Option B - $f^{-1}(x)=\frac{-4-3x}{x-7}$

Step-by-step explanation:

Given : $f(x)=\frac{7x-4}{x+3}$

To find : Find the inverse of the function ?

Solution :

Let y=f(x)

$y=\frac{7x-4}{x+3}$

Replace y with x,

$x=\frac{7y-4}{y+3}$

$x(y+3)=7y-4$

$xy+3x=7y-4$

$xy-7y=-4-3x$

$y(x-7)=-4-3x$

$y=\frac{-4-3x}{x-7}$

i.e. $f^{-1}(x)=\frac{-4-3x}{x-7}$

Therefore, Option B is correct.