Answer:
[tex]f(8) = 81[/tex]
[tex](g\ o\ f)(x) = x^2 + 2x -4[/tex]
Step-by-step explanation:
Solving (a):
[tex]f(x) = x^2 + 2x +1[/tex]
[tex]g(x) = x - 5[/tex]
Solve for f(8)
We have:
[tex]f(x) = x^2 + 2x +1[/tex]
Substitute 8 for x
[tex]f(8) = 8^2 + 2*8 +1[/tex]
Solve
[tex]f(8) = 64 + 16 +1[/tex]
[tex]f(8) = 81[/tex]
Solving (b):
[tex](g\ o\ f)(x)[/tex]
This is solved by:
[tex](g\ o\ f)(x) = g(f(x))[/tex]
So, we have:
[tex]g(x) = x - 5[/tex]
[tex]g(f(x)) = f(x) - 5[/tex]
Substitute: [tex]f(x) = x^2 + 2x +1[/tex]
[tex]g(f(x)) = x^2 + 2x + 1 - 5[/tex]
[tex]g(f(x)) = x^2 + 2x -4[/tex]
Hence:
[tex](g\ o\ f)(x) = x^2 + 2x -4[/tex]
