Answer:
[tex](f o g)(x) = 2x + 9[/tex]
[tex](g o f)(x) = 2x + 15[/tex]
[tex](f o g)(2) = 11[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x+6[/tex]
[tex]g(x) = 2x + 3[/tex]
Solving (a): (f o g)(x)
In functions:
[tex](f o g)(x) = f(g(x))[/tex]
Solving for f(g(x))
[tex]f(x) = x+6[/tex]
[tex]f(g(x)) = 2x + 3 + 6[/tex]
[tex]f(g(x)) = 2x + 9[/tex]
So:
[tex](f o g)(x) = 2x + 9[/tex]
Solving (a): (g o f)(x)
In functions:
[tex](g o f)(x) = g(f(x))[/tex]
Solving for g(f(x))
[tex]g(x) = 2x + 3[/tex]
[tex]g(f(x)) = 2(x+6)+3[/tex]
Open bracket
[tex]g(f(x)) = 2x+12+3[/tex]
[tex]g(f(x)) = 2x+15[/tex]
So:
[tex](g o f)(x) = 2x + 15[/tex]
Solving (c): (f o g)(2)
In (a):
[tex](f o g)(x) = 2x + 9[/tex]
Substitute 2 for x
[tex](f o g)(2) = 2*2 + 9[/tex]
[tex](f o g)(2) = 4 + 9[/tex]
[tex](f o g)(2) = 11[/tex]
