Mathematics 10 — Exercise Review · Q3 (iv)

Full question

For the following functions, find (gog)(x).

Step-by-step solution

1. Composition means apply the inner function first, then use its entire output as the input of the outer function.

   $$2\times x+14$$

2. Replace every x of the outer function by this full bracketed inner expression.

   $$2\times \left(2\times x+14\right)+14$$

3. Substitute the function expressions, keeping the brackets.

   $$2\times \left(2\times x+14\right)+14$$

4. Distribute each bracket product: each term multiplies every term in the other bracket.

   $$4\times x+42$$

5. Write EVERY distributed product before collecting terms.

   $$14+2\times 14+2\times 2\times x$$

6. Calculate this individual product, including its sign and powers.

   $$14=14$$

7. Calculate this individual product, including its sign and powers.

   $$2\times 14=28$$

8. Calculate this individual product, including its sign and powers.

   $$2\times 2\times x=4\times x$$

9. These terms have the same variable part. Add ONLY their coefficients.

   $$14+28=42$$

10. These terms have the same variable part. Add ONLY their coefficients.

    $$4=4$$

11. Put the simplified groups together.

    $$4\times x+42$$

12. Collect terms with the same power and simplify their coefficients.

    $$4\times x+42$$

Answer

The final answer is shown below.