Given:
[tex]\begin{gathered} f(x)=x^2+6 \\ g(x)=\frac{x+8}{x} \end{gathered}[/tex]We want ( g º f )( – 7), which means we plug in the function "f" into "g". Then substitute "-7" into "x" of the new function. Check the working below:
[tex]\begin{gathered} \mleft(gºf\mright)\mleft(x\mright)=\frac{(x^2+6)+8}{(x^2+6)} \\ (gºf)(x)=\frac{x^2+14}{x^2+6} \\ (gºf)(-7)=\frac{(-7)^2+14}{(-7)^2+6} \\ =\frac{49+14}{49+6} \\ =\frac{63}{55} \end{gathered}[/tex]
