Question

For questions 5-6 the functions are
f(x)=5x^2+3
g(x)=x^2-7

Answer 1

see explanation

Explanation:

Note that

(f + g)(x) = f(x) + g(x) and

(f - g)(x) = f(x) - g(x)

5

f(x) + g(x)

= 5x² + 3 + x² - 7 = 6x² - 4

6

f(x) - g(x) = 5x² + 3 - (x² - 7) ← distribute parenthesis

= 5x² + 3 - x² +7 ← collect like terms

= 4x² + 10

7

f(x) + g(x) =
`4^(x)` + 3x + 2x - 5 =
`4^(x)` + 5x - 5