Question

Problem 3. if f(x) = /2x-5 and g(x) = 5x? -- 3, find (gºf)(x). (Step by step please<3)

Answer 1

(1) f(x) = x² - 4x + 2, g(x) = 3x - 7

(f o g) (x) = f(g(x)) = f (3x - 7)

= (3x - 7)² - 4(3x - 7) + 2

= (9x² - 42x + 49) + (-12x + 28) + 2

= 9x² - 57x + 79

(2) g(x) = -6x + 5, h(x) = -9x - 11

(g o h) (x) = g(h(x)) = g (-9x - 11)

= -6(-9x - 11) + 5

= 54x + 66 + 5

= 54x + 71

(3) f(x) = √(2x - 5), g(x) = 5x² - 3

(g o f) (x) = g(f(x)) = g(√(2x - 5))

= 5 (√(2x - 5))² - 3

= 5 (2x - 5) - 3

= 10x - 25 - 3

= 10x - 28