VERIFYING INVERESE FUNCTIONS BY COMPOSITION

Check the pair of functions are inverses to each other.

Example 1 :

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

Solution :

Finding (f∘g) (x) :

(f∘g) (x) = f(g(x))

Finding (g∘f) (x) :

(g∘f) (x) = g(f(x))

So, the functions f(x) and g(x) are inverse to each other.

Example 2 :

f(x) = x³ + 1 and g(x) = ∛(x-1)

Solution :

Finding (f∘g) (x) :

(f∘g) (x) = f(g(x))

Finding (g∘f) (x) :

(g∘f) (x) = g(f(x))

So, the functions f(x) and g(x) are inverse to each other.

Example 3 :

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

Solution :

Finding (f∘g) (x) :

(f∘g) (x) = f(g(x))

Finding (g∘f) (x) :

(f∘g) (x) = f(g(x))

So, the functions f(x) and g(x) are inverse to each other.

Example 4 :

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

Solution :

Finding (f∘g) (x) :

(f∘g) (x) = f(g(x))

Finding (g∘f) (x) :

(g∘f) (x) = g(f(x))

So, the functions f(x) and g(x) are inverse to each other.