FIND COMPOSITION OF TWO FUNCTIONS

Problem 1 :

Given f(x) = -9x + 3 and g(x) = x⁴, find (f ∘ g)(x)

Solution :

(f ∘ g)(x) = f(g(x))

= f(x⁴)

= -9(x⁴) + 3

(f ∘ g)(x) = -9x⁴ + 3

Problem 2 :

Given f(x) = 2x – 5 and g(x) = x + 2, find (f ∘ g)(x)

Solution :

(f ∘ g)(x) = f(g(x))

= f(x + 2)

= 2(x + 2) – 5

= 2x + 4 – 5

= 2x - 1

 (f ∘ g)(x) = 2x - 1

Problem 3 :

Given f(x) = x² + 7 and g(x) = x - 3, find (f ∘ g)(x)

Solution :

(f ∘ g)(x) = f(g(x))

= f(x - 3)

= (x - 3)² + 7

= x² + (3)² – 2(x)(3) + 7

= x² + 9 - 6x + 7

 (f ∘ g)(x) = x² - 6x + 16

Problem 4 :

Given f(x) = 4x + 3 and g(x) = x², find (g ∘ f)(x)

Solution :

(g ∘ f)(x) = g(f(x))

= g(4x + 3)

= (4x + 3)²

= (4x)² + (3)² + 2(4x)(3)

= 16x² + 9 + 24x

 (g ∘ f)(x) = 16x² + 24x + 9

Problem 5 :

Given f(x) = x – 1 and g(x) = x² + 2x - 8, find (g ∘ f)(x)

Solution :

(g ∘ f)(x) = g(f(x))

= g(x - 1)

= (x – 1)² + 2(x – 1) - 8

= (x)² + (1)² – 2(x)(1) + 2x – 2 - 8

= x² + 1 - 2x + 2x - 10

 (g ∘ f)(x) = x² - 9