Mathematics 10 — Exercise 4.1 · Q1 (ii)

Full question

For the following functions, find f-g.

Step-by-step solution

1. Substitute the function expressions, keeping the brackets.

   $$2\times x+5-(3\times x-2)$$

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

   $$7-x$$

3. Write EVERY distributed product before collecting terms.

   $$5+2\times x--2-3\times x$$

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

   $$5=5$$

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

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

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

   $$\left(-1\right)\times \left(-2\right)=2$$

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

   $$-3\times x=-3\times x$$

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

   $$5+2=7$$

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

   $$2-3=-1$$

10. Put the simplified groups together.

    $$7-x$$

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

    $$7-x$$

Answer

The final answer is shown below.