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

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.

   $$x^3$$

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

   $${\left(x^3\right)}^3$$

3. Substitute the function expressions, keeping the brackets.

   $${\left(x^3\right)}^3$$

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

   $${\left(x^3\right)}^3$$

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

   $$x^9$$

Answer

The final answer is shown below.