FINDING COMPOSITION OF FUNCTIONS WORKSHEET

Find the composition of the functions given below.

1)  If f(x) = 3x - 5 and g(x) = x², find (f∘g) (x).

Solution

2)  Let f(x) = -3x + 7 and g(x) = 2x² - 8, find (f∘g) (x) and (g∘f) (x).           Solution

3) If f(x) = -9x - 9 and g(x) = √(x - 9), find (f∘g) (x).

Solution

4)  If f(x) = -2x + 1 and g(x) = √(x² - 9), find

(i)  (f∘g) (x) and 

(ii)  (g∘f) (x)                   Solution

5)  If f(x) = -2x + 1 and g(x) = √(x² - 5), find

(i)  (f∘g) (x) and 

(ii)  (g∘f) (x)                 Solution

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

Solution

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

Solution

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

Solution

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

Solution

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

Solution

Composition of Functions with Square Roots

1)  Let f(x) = x² - 1 and let g(x) = √x. Find the domain of the composition functions

(i)  g∘f 

(ii)  f∘g              Solution

2)  Let

f(x) = 1/(x² - 1) and g(x) = √(x - 2)

Find the domain of f(g(x))              Solution

3)  Let

f(x) = √(x + 2) and g(x) = x²

Find the domain of f(g(x)).          Solution

Verifying Inverse Functions By Compositions

Check the pair of functions are inverses to each other.

1)  f(x) = 4x + 3 and g(x) = (x - 3)/4            Solution

2)  f(x) = x³ + 1 and g(x) = ∛(x-1)             Solution

3)  f(x) = √(x - 3) and g(x) = x² + 3, x ≥ 0          Solution

4)  f(x) = (4x + 4)/(x + 5) and g(x) = (4 - 5x)/(x - 4)

Solution