Question

If f(x)=(3x-4)/(5x-3); find f^(-1) .​

Answer 1

Step-by-step explanation:

Given:-

f(x)=(3x-4)/(5x-3)

To find:-

Find f^(-1) ?

Solution:-

Given equation is f(x)=(3x-4)/(5x-3)

Let y = f(x)

=>x => f^-1(y)

=>y = (3x-4)/(5x-3)

=>y(5x-3) = 3x-4

=>5xy -3y = 3x -4

=>5xy -3y -3x = -4

=>(5xy-3x)-3y = -4

=>x(5y-3)-3y = -4

=>x(5y-3) = 3y-4

=>x = (3y-4)/(5y-3)

=>f^-1(y) = (3y-4)/(5y-3)

Now, f^-1(x) = (3x-4)/(5x-3)

=>f^-1(x)=y

Now put x = 1 then

=>f^-1(1) = (3(1)-4)/(5(1)-3)

=>(3-4)/(5-3)

=>-1/2

and

Put x = -1 then

f^(-1) = (3(-1)-4)/(5(-1)-3)

=>(-3-4)/(-5-3)

=>-7/-8

=>7/8

Answer:-

f^-1(x) = (3x-4)/(5x-3)

f^-1(1) = -1/2

f^(-1) = 7/8 for the given problem