Question

Help please out due to medical issues trying to catch up and learn for my upcoming test

Answer 1

The functions given in the question are

`f(x)=7x-7,g(x)=x^2-7x+6`

Step 1:

To figure out (fog)(x), we will substitute the value of x=x²-7x+6 in f(x)

`\begin{gathered} f(x)=7x-7, \\ f(g)(x)=7(x^2-7x+6)-7 \\ f(g)(x)=7x^2-49x+42-7 \\ f(g)(x)=7x^2-49x+35 \end{gathered}`

Hence,

The function for (fog)(x) will be

`\Rightarrow7x^2-49x+35`

Step 2:

To figure out (gof)(x), we will substitute the value of x=7x-7in g(x)

`\begin{gathered} g(x)=x^2-7x+6 \\ g(f(x)=(7x-7)^2-7(7x-7)+6 \\ g(f(x)=(7x-7)(7x-7)-49x+49+6 \\ g(f(x)=49x^2-49x-49x+49-49x+49+6 \\ g(f(x)=49x^2-147x+104 \end{gathered}`

Hence,

The value for (gof)(x) will be

`\Rightarrow49x^2-147x+104`