given; f (x) = 4x - 5, g (x) = x² + 4 and h (x) = x + 6
a. ( f ° g ) (x)
b. ( g ° f ) (x)
c. ( f ° h ) (7)
d. ( g ° h ) (5)
Answer (1)
Answer:Here are the solutions: - f(x) = 4x - 5- g(x) = x^2 + 4 + 6 = x^2 + 10- h(x) = x a. (f \circ g)(x)(f \circ g)(x) = f(g(x)) = f(x^2 + 10) = 4(x^2 + 10) - 5 = 4x^2 + 40 - 5 = 4x^2 + 35 b. (g \circ f)(x)(g \circ f)(x) = g(f(x)) = g(4x - 5) = (4x - 5)^2 + 10 = 16x^2 - 40x + 25 + 10 = 16x^2 - 40x + 35 c. (f \circ h)(7)(f \circ h)(7) = f(h(7)) = f(7) = 4(7) - 5 = 28 - 5 = 23 d. (g \circ h)(5)(g \circ h)(5) = g(h(5)) = g(5) = (5)^2 + 10 = 25 + 10 = 35
