Mathematics 10 — Exercise 4.1 · Q7 (ii)

Full question

For f(x)=4x+2 and g(x)=6x−18, solve f⁻¹(x)=g⁻¹(x).

Step-by-step solution

1. Use the inverses already found. Set them equal.

   $$\frac{x}{4}-\frac{1}{2}=\frac{x}{6}+3$$

2. Multiply both sides by 12 to clear both denominators.

   $$3\times x-6=2\times x+36$$

3. Expand both brackets.

   $$3\times x-6=2\times x+36$$

4. Equate the corresponding entries.

   $$3\times x-6=2\times x+36$$

5. Collect the variable terms on the left and constants on the right.

   $$x=36+6$$

6. Simplify the constant calculation.

   $$x=42$$

7. Divide both sides by the variable coefficient.

   $$x=42\times \frac{1}{1}$$

8. Reduce the fraction.

   $$x=42$$

Answer

The final answer is shown below.