Respuesta :

[tex]\bf \begin{cases} f(x)=4x-1\\ g(x)=x^2+7 \end{cases}~\hspace{7em}g(~~~f(x)~~~)=[~f(x)~]^2+7 \\\\\\ g(~~~f(x)~~~)=[~4x-1~]^2+7\implies g(~~~f(x)~~~)=(4x-1)(4x-1)+7 \\\\\\ g(~~~f(x)~~~)=\stackrel{\mathbb{F ~O~ I~ L}}{(16x^2-8x+1)}+7\implies g(~~~f(x)~~~)=16x^2-8x+8[/tex]

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Answer

[tex]g(f(x)) = = 16 {x}^{2} - 8x + 8[/tex]

step by step Explanation

The functions given are

[tex]f (x)= 4x- 1[/tex]

[tex]g(x)= {x}^{2} + 7[/tex]

We want to find:

[tex]g(f (x))= g( 4x- 1)[/tex]

This implies that

[tex]g(f (x))= ( (4x- 1)^{2} + 7) [/tex]

Let us now simplify

[tex]( {a - b)}^{2} = {a}^{2} -2ab + {b}^{2} [/tex]

This implies that

[tex] ( (4x- 1)^{2} + 7) =( {(4x)}^{2} - 2(4x) \times 1 + 1 [/tex]

Combine the terms to get,

[tex] = 16 {x}^{2} - 8x + 1 + 7[/tex]

[tex] = 16 {x}^{2} - 8x + 8[/tex]

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