Respuesta :

ghanami
hello :
s(x)=x-7 and t(x)=4x²-x+3
(t•s)(x) = t(s(x)) = t(x-7) = 4(x-7)²-(x-7) +3
(t•s)(x) = 4(x-7)²-x+7+3

Answer:  (B) [tex] 4(x-7)^2-(x-7)+3.[/tex]

Step-by-step explanation:  We are given the following two functions :

[tex]s(x)=x-7,\\\\t(x)=4x^2-x+3.[/tex]

We are to find the expression that is equivalent to [tex](t.s)(x).[/tex]

We know that

for any two functions f(x) and g(x), we have

[tex](f.g)(x)=f(g(x)).[/tex]

Therefore, we get

[tex](t.s)(x)\\\\=t(s(x))\\\\=t(x-7)\\\\=4(x-7)^2-(x-7)+3.[/tex]

Thus, [tex](t.s)(x)[/tex] is equivalent to [tex] 4(x-7)^2-(x-7)+3.[/tex]

Option (B) is CORRECT.

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