Pre calculus Hw

Question

Use

f(x) = 4x − 5

and

g(x) = 2 − x2

to evaluate the expression.

(a) (f ∘ f)(x)

(b) (g ∘ g)(x)

Answer 1

Domain* - basically wherever x values your function can go, so 1/x does not exist at x = 0, so the domain would be (-∞, 0) U (0, ∞)

f(x) = 4x − 5, g(x) = 2 - x²

a)

(f ∘ f)(x) = f(f(x)) = f(4x - 5) = 4(4x - 5) - 5 = 16x - 20 - 5 = 16x - 25

Domain: (-∞, ∞)

b)

(g ∘ g)(x) = g(g(x)) = g(2 - x²) = 2 - (2 - x²)² = 2 - (4 - 4x² + x⁴) = -2 + 4x² - x⁴

Domain: (-∞, ∞)