If f(x) = 1 / (3x – 5), what is the inverse of f?

Answer 1

The easiest way to find the inverse is to swap the x and y.

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

-change f(x) to y

y=1/(3x-5)

-at this stage, swap x and y

x=1/(3y-5)

-Now solve for y

x=1/(3y-5) (multiply both sides by (3y-5)

x(3y-5)=1 (divide both sides by x)

3y-5=1/x (add 5 to both sides)

3y=1/x + 5 (divide both sides by 3)

y=(1/x+5)/3

We can further simplify this into a single fraction as

y= (1+5x)/(3x)

so

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