Mathematics 10 — Exercise 4.1 · Q3 (i) (a)

Full question

For the following functions, find (fog)(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.

   $$x^3$$

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

   $$2\times x^3+3$$

3. Substitute the function expressions, keeping the brackets.

   $$2\times x^3+3$$

4. Remove the brackets. A preceding minus sign reverses every sign inside that bracket.

   $$2\times x^3+3$$

5. Write EVERY distributed product before collecting terms.

   $$2\times x^3+3$$

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

   $$3=3$$

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

   $$2\times x^3=2\times x^3$$

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

   $$3=3$$

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

   $$2=2$$

10. Put the simplified groups together.

    $$2\times x^3+3$$

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

    $$2\times x^3+3$$

Answer

The final answer is shown below.