Question

How do you find the inverse of `f(x)= 5x + 10`?

Answer 1

The inverse of a function is the relation that is formed when the function is transformed over the line `y = x`

Explanation:

The inverse can be found algebraically by switching x for y and y for x in the equation. You must then isolate y.

`f(x) = 5x + 10`

`y = 5x + 10`

`x = 5y + 10`

`x - 10 = 5y`

`(x - 10)/5 = y`

So, `f^-1(x) = (x - 10)/5`

Practice exercises:

1. Find the inverse of the following functions:

a) `f(x) = 3x + 4`

b) `g(x) = sqrt(4x - 1)`

c) `h(x) = 2/(2x - 3)`

Good luck!