The composition of a function g with a function f is :
h(x) = g(f (x))
The domain of h is the set of all x-values such that x is in the domain of f and f (x) is in the domain of g.
Problem 1 :
Given f(x) = -9x + 3 and g(x) = x^{4}, find (f ∘ g)(x)
Solution :
(f ∘ g)(x) = f(g(x))
= f(x^{4})
= -9(x^{4}) + 3
(f ∘ g)(x) = -9x^{4} + 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) = x^{2} + 7 and g(x) = x - 3, find (f ∘ g)(x)
Solution :
(f ∘ g)(x) = f(g(x))
= f(x - 3)
= (x - 3)^{2} + 7
= x^{2} + (3)^{2} – 2(x)(3) + 7
= x^{2} + 9 - 6x + 7
(f ∘ g)(x) = x^{2} - 6x + 16
Problem 4 :
Given f(x) = 4x + 3 and g(x) = x^{2}, find (g ∘ f)(x)
Solution :
(g ∘ f)(x) = g(f(x))
= g(4x + 3)
= (4x + 3)^{2}
= (4x)^{2} + (3)^{2} + 2(4x)(3)
= 16x^{2} + 9 + 24x
(g ∘ f)(x) = 16x^{2} + 24x + 9
Problem 5 :
Given f(x) = x – 1 and g(x) = x^{2} + 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
= x^{2} + 1 - 2x + 2x - 10
(g ∘ f)(x) = x^{2} - 9
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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