Question

F(x) = x^2 + 6 and g(x) X + 8 /x Find (gºf)( – 7).

Answer 1

Given:

`\begin{gathered} f(x)=x^2+6 \\ g(x)=(x+8)/(x) \end{gathered}`

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:

`\begin{gathered} \mleft(gºf\mright)\mleft(x\mright)=((x^2+6)+8)/((x^2+6)) \\ (gºf)(x)=(x^2+14)/(x^2+6) \\ (gºf)(-7)=((-7)^2+14)/((-7)^2+6) \\ =(49+14)/(49+6) \\ =(63)/(55) \end{gathered}`

​