Given
[tex]\begin{gathered} f(x)=\text{ 6x-4} \\ g(x)=3x^2-2x-10 \end{gathered}[/tex]
Solution
[tex]\begin{gathered} \text{gof(x)}=g(6x-4) \\ \text{gof(x)}=3(6x-4)^2-2(6x-4)-10 \\ \end{gathered}[/tex]
Expand the bracket
[tex]\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}[/tex]
The final answer
[tex]\text{gof(x)}=108x^2-156x+46[/tex]
