Mathematics 10 — Exercise Review · Q2 (i)

Full question

For the following functions, find f+g.

Step-by-step solution

1. Substitute the function expressions, keeping the brackets.

   $$-(x^2-25)+x+5$$

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

   $$-(x^2-25)+x+5$$

3. Write EVERY distributed product before collecting terms.

   $$25-x^2+5+x$$

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

   $$25=25$$

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

   $$-x^2=-x^2$$

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

   $$5=5$$

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

   $$x=x$$

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

   $$25+5=30$$

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

   $$-1=-1$$

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

    $$1=1$$

11. Put the simplified groups together.

    $$30-x^2+x$$

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

    $$-x^2+x+30$$

Answer

The final answer is shown below.