Answer:
The functions given in the question are
[tex]f(x)=7x-7,g(x)=x^2-7x+6[/tex]
Step 1:
To figure out (fog)(x), we will substitute the value of x=x²-7x+6 in f(x)
[tex]\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}[/tex]
Hence,
The function for (fog)(x) will be
[tex]\Rightarrow7x^2-49x+35[/tex]
Step 2:
To figure out (gof)(x), we will substitute the value of x=7x-7in g(x)
[tex]\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}[/tex]
Hence,
The value for (gof)(x) will be
[tex]\Rightarrow49x^2-147x+104[/tex]
