Mathematics 10 — Exercise Review · Q8 (ii)

Full question

For f(x)=3x+7, solve f(x)=f⁻¹(x).

Step-by-step solution

1. Use f⁻¹(x)=(x−7)/3 and equate it to f(x)=3x+7.

   $$3\times x+7=\frac{x}{3}-\frac{7}{3}$$

2. Multiply both sides by 3.

   $$9\times x+21=x-7$$

3. Expand the left bracket.

   $$9\times x+21=x-7$$

4. Equate the corresponding entries.

   $$9\times x+21=x-7$$

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

   $$8\times x=-7-21$$

6. Simplify the constant calculation.

   $$8\times x=-28$$

7. Divide both sides by the variable coefficient.

   $$x=-\frac{28}{8}$$

8. Reduce the fraction.

   $$x=-\frac{7}{2}$$

Answer

The final answer is shown below.