Evaluate the composite function where gx x2 5x and hx 5 3x

Evaluate the composite function, where g(x) = x2 5x and h(x) = 5 3x2. (h g)(0)

Solution

g(x) = x² - 5x

h(x) = 5 - 3x²

h o g = h(g(x)) = 5 - 3(x² - 5x)² = 5 - 3(x⁴ - 10x³ + 25x²) = 5 - 3x⁴ + 30x³ - 75x²

h o g = 5 - 3x⁴ + 30x³ - 75x²

h o g (0) = 5 - 3(0)⁴ + 30(0)³ - 75(0)² = 5