Question

Let f(x) =4x-1 and g(x) = 2x^2 + 3 (fg)(x) , f/g(x), g/f(x)

Answer 1

f(x) = 4x - 1
g(x) - 2x² + 3

(f · g)(x)
(f · g)(x) = (4x - 1)(2x² + 3)
(f · g)(x) = 4x(2x² + 3) - 1(2x² + 3)
(f · g)(x) = 4x(2x²) + 4x(3) - 1(2x²) - 1(3)
(f · g)(x) = 8x³ + 12x - 2x² - 3

(f/g)(x)
(f/g)(x) = 4x - 1
2x² + 3

(g/f)(x)
(g/f)(x) = 2x² + 3
4x - 1
(g/f)(x)= ¹/₂x + ¹/₈ + 3¹/₈
4x - 1