Mathematics 10 — Exercise 4.1 · Q3 (ii) (c)

Full question

For the following functions, find (fof)(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.

   $$\frac{2}{x}$$

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

   $$\frac{2}{\frac{2}{x}}$$

3. Substitute the function expressions, keeping the brackets.

   $$\frac{2}{\frac{2}{x}}$$

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

   $$x$$

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

   $$x$$

6. Retain inputs where the inner function is defined and where its output makes the outer function defined. Neither denominator may be zero.

   $$(x\ne 0,1\ne 0)$$

Answer

The final answer is shown below.