Concept explainers
Given the functions f(x) = 2x + 3 and g(x) = 2x2 – 4x, find
- a. (f ∘ g)(x)
- b. (g ∘ f)(x)
- c. (f ∘ g)(3)
- d. (g ∘ f)(−2)
- e. (f ∘ f)(1)
a.
The composite function
Answer to Problem 1PCT
The value of the composite function
Explanation of Solution
Definition used:
Given two functions f and g, the composite function, denoted by
Calculation:
The given functions are,
By using the above definition, find the value of the composite function
Thus, the value of the composite function
b.
The composite function
Answer to Problem 1PCT
The value of the composite function
Explanation of Solution
The given functions are
By using the above definition, find the value of the composite function
Thus, the value of the composite function
c.
The composite function
Answer to Problem 1PCT
The value of
Explanation of Solution
From part (a) it is observed that, the value of the composite function
Substitute
Thus, the value of
d.
The composite function
Answer to Problem 1PCT
The value of
Explanation of Solution
From part (b) it is observed that, the value of the composite function
Substitute
Thus, the value of
e.
The composite function
Answer to Problem 1PCT
The value of the composite function
Explanation of Solution
The given functions are,
By using the above definition, find the value of the composite function
That is,
Substitute
Thus, the value of the composite function
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