The value of given composite functions (h o g) (n) is 12n + 1. Option C is correct.
First, let us understand the composite function:
In mathematics, function composition is an operation ∘ that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g(f(x)).
The given function (h o g) is a composite function.
We are given;
h(n) = 4n - 3
g(n) = 3n + 1
We need to find (h o g) (n).
Substitute the value of n with g(n) in h(n), we will get:
(h o g) (n) = 4 * g(n) - 3
(h o g) (n) = 4 * (3n + 1) - 3
(h o g) (n) = 12n + 4 - 3
(h o g) (n) = 12n + 1
So, (h o g) (n) = 12n + 1.
Option C is correct.
Thus, the value of given composite functions (h o g) (n) is 12n + 1. Option C is correct.
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