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If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?

A) 6 – 3 – (4 + 3)2

B) 6 – 3 – (4 – 32)

C) 6(3) – 4 + 32

D) 6(3) – 4 – 32

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Answer:  The correct option is

(C) [tex]6(3)-4+3^2.[/tex]

Step-by-step explanation:  We are given two functions f(x) and g(x) as follows :

[tex]f(x)=4-x^2,\\\\g(x)=6x.[/tex]

We know that for any two functions p(x) and q(x), we have

[tex](p-q)(x)=p(x)-q(x).[/tex]

Therefore, we get

[tex](g-f)(x)=g(x)-f(x)=6x-(4-x^2)=6x-4+x^2\\\\\\\Rightarrow (g-f)(3)=6(3)-4+3^2.[/tex]

Thus, (C) is the correct option.

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