Answer:
answers for only 2 and 4
Step-by-step explanation:
2. f(g)(x) = 4(x^2 - 5x + 3) + 1
= 4x^2 - 20x + 12 + 1
= 4x^2 - 20x + 13
4. h(7) = 7-2=5
g(h)(7) = 7^2 + 3
=49 + 3
=52
Answer:
see explanation
Step-by-step explanation:
(2)
(f • g)(x) = f(x) × g(x), that is
(4x - 1)(x² - 5x + 3)
= 4x(x² - 5x + 3) - 1 (x² - 5x + 3) ← distribute parenthesis
= 4x³ - 20x² + 12x - x² + 5x - 3 ← collect like terms
= 4x³ - 21x² + 17x - 3
(3)
Factor both g(x) and f(x)
g(x) = 3x - 12 = 3(x - 4) ← common factor of 3
f(x) = x² + x - 20 = (x + 5)(x - 4), thus
[tex]\frac{g(x)}{f(x)}[/tex]
= [tex]\frac{3(x-4)}{(x+5)(x-4)}[/tex]
Cancel the factor (x - 4) on the numerator and denominator
= [tex]\frac{3}{x+5}[/tex]
The denominator cannot be zero as this would make rational function undefined, thus
domain is x ∈ R , x ≠ - 5
(4)
To evaluate (g ￮ h)(7), evaluate h(7) then use this result to evaluate g(x)
h(7) = 7 - 2 = 5, then
g(5) = 5² + 3 = 25 + 3 = 28
