Mathematics 10 — Exercise Review · Q4 (iv)

Full question

Find the inverse function f⁻¹(x) of the following function f(x), stating any restrictions on its domain.

Step-by-step solution

1. Write the output as y. To find the inverse, solve this equation for the original input x.

   $$y=\frac{3}{2}-\frac{x}{2}$$

2. Subtract the constant from both sides.

   $$y-\frac{3}{2}=-\frac{x}{2}$$

3. Divide both sides by the input coefficient.

   $$x=\frac{y-\frac{3}{2}}{-\frac{1}{2}}$$

4. Interchange the names x and y: the old output is now the inverse input.

   $$\mathrm{f⁻¹}\left(x\right)=3-2\times x$$

5. The inverse domain is the original range. Keep any exclusions or nonnegative-input restriction.

   $$\mathrm{ℝ}$$

Answer

The final answer is shown below.