High School

Given the functions \( f(x) = 9x - 3 \) and \( g(x) = 3x + 4 \), find \( f \cdot g \).

A) \( 27x^2 - 12 \)

B) \( 12x^2 + 27x + 1 \)

C) \( 27x^2 + 27x - 12 \)

D) \( 27x^2 - 5x - 12 \)

Answer :

The composition of f and g, represented as (f∘g)(x), is found by substituting g(x) into f(x), by which we obtain 27x + 33 as the result, which isn't listed among the provided options.

The subject of this question is mathematics, specifically the topic of function composition.

Given two functions f(x) =9x - 3 and g(x) =3x + 4, the student is asked to find fg, also known as the composition of the functions f and g.

This means applying the function g to the function f, represented as (f∘g)(x).

The composition of f and g is found by substituting g(x) into f(x) which is denoted as (f∘g)(x) = f(g(x)).

So, plugging g(x) into our function f(x), we get-

[tex](f∘g)(x) = f(3x+4) \\= 9*(3x+4) - 3 \\= 27x +36 - 3 \\= 27x + 33[/tex]

Therefore, none of the given options seems to be the correct solution for the composite function fg.

Learn more about the topic of Function Composition here:

https://brainly.com/question/30660139

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