Question

Find the inverse of the function f(x) = 2x – 4.

Answer 1

The inverse of the function f(x) = 2x – 4 is  $\mathbf{f^{-1}(x) = \dfrac{x}{2}+2}$

An inverse of a given function is achieved by replacing the value of x with y, followed by changing the rhythm of the arithmetic operation.

For example; If f(x) posits that we divide three and then add two, the inverse of f(x) will be to remove two then followed by dividing it by three.

From the given information:

$\mathbf{f(x) = 2x - 4}$

The inverse of the function will be:

• to replace x with y

Now;

y = 2x - 4

Divide the right-hand side by 2 and changing the arithmetic sign, we have:

$\mathbf{y = \dfrac{x}{2}+ 2}$

∴

$\mathbf{f^{-1}(x) = \dfrac{x}{2}+2}$

Therefore, we can conclude that the inverse of the function f(x) = 2x – 4 is $\mathbf{f^{-1}(x) = \dfrac{x}{2}+2}$

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