Question

If x is multiplied by 5 and then 3 is subtracted, then the function isf(x) = 5x -3.What are the steps to find the inverse to this function?

Answer 1

Step:

Concept:

First, find the inverse of subtraction which is addition

x + 3

Step 2:

The multiplicative inverse is division, hence, you will divide x + 3 by 5.

Therefore, we have

$\begin{gathered} y\text{ = }\frac{x\text{ + 3}}{5} \\ \end{gathered}$

The inverse of the function is given below.

$f^{-1}(x)\text{ = }\frac{x\text{ + 3}}{5}$

Method 2

$\begin{gathered} \text{If f(x) = 5x - 3} \\ \text{let y = 5x - 3} \\ \text{Make x subject of the formula} \\ \text{y + 3 = 5x} \\ x\text{ = }\frac{y\text{ + 3}}{5} \\ \text{Write the inverse of f(x) by changing y to x} \\ f^{-1}(x)\text{ = }\frac{x\text{ + 3}}{5} \end{gathered}$