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F(x) = 6x - 4g(x) = 3x² – 2x – 10Write (gof)(x) as an expression in terms of x.(gof)(x) =

F(x) = 6x - 4g(x) = 3x² – 2x – 10Write (gof)(x) as an expression in terms of x.(gof)(x) =
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F(x) = 6x - 4g(x) = 3x² – 2x – 10Write (gof)(x) as an expression in terms of x.(gof)(x) =

F(x) = 6x - 4g(x) = 3x² – 2x – 10Write (gof)(x) as an expression in terms of x.(gof-example-1
asked
User Christian Meinerding
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8.6k points

1 Answer

4 votes

Given


\begin{gathered} f(x)=\text{ 6x-4} \\ g(x)=3x^2-2x-10 \end{gathered}

Solution


\begin{gathered} \text{gof(x)}=g(6x-4) \\ \text{gof(x)}=3(6x-4)^2-2(6x-4)-10 \\ \end{gathered}

Expand the bracket


\begin{gathered} \text{gof(x)}=3(6x-4)(6x-4)^{}-2(6x-4)-10 \\ \text{gof(x)}=3(36x^2-48x_{}+16)^{}-2(6x-4)-10 \\ \text{open the bracket} \\ \\ \text{gof(x)}=108x^2-144x_{}+48^{}-12x+8-10 \\ \text{gof(x)}=108x^2-144x_{}+48^{}-12x-2 \\ \text{gof(x)}=108x^2-144x_{}-12x+48-2 \\ \\ \text{gof(x)}=108x^2-144x_{}-12x+46 \\ \text{gof(x)}=108x^2-156x+46 \end{gathered}

The final answer


\text{gof(x)}=108x^2-156x+46

answered
User Syed Salman Akbar
by
8.3k points
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