Question

What is `f^-1(3)` when `f(x) = (2x + 3) / 5`?

Answer 1

# f^-1(3) = 6

Explanation:

To find the inverse function. Change the subject to x.

let y = f(x)

then `y = (2x + 3 )/5`

hence 2x + 3 = 5y and x =`1/2 (5y - 3 )`

( This enables x to be found when y is known )

Although it is written as y = , it is usual to have it expressed
in terms of x.

`rArr f^-1(x) = 1/2 (5x -3 )`

and `f^-1(3) = 1/2 (15 - 3 ) = 6`