Answer:
[tex]g(-3) = 5[/tex]
[tex]f(2) = 13[/tex]
[tex](f + g)(x) = x^2 +2x- 1[/tex]
Step-by-step explanation:
Solving (a):
[tex]g(x) = x^2 - 4[/tex]
Required
Determine g(-3)
[tex]g(x) = x^2 - 4[/tex]
Substitute -3 for x
[tex]g(-3) = (-3)^2 - 4[/tex]
[tex]g(-3) = 9- 4[/tex]
[tex]g(-3) = 5[/tex]
Solving (b):
[tex]f(x) = 3x + 7[/tex]
Required
Determine f(2)
[tex]f(x) = 3x + 7[/tex]
Substitute 2 for x
[tex]f(2) = 3*2 + 7[/tex]
[tex]f(2) = 6 + 7[/tex]
[tex]f(2) = 13[/tex]
Solving (c):
[tex]f(x) = 2x + 3[/tex]
[tex]g(x) = x^2 - 4[/tex]
Required
[tex](f + g)(x)[/tex]
In functions:
[tex](f + g)(x) = f(x) + g(x)[/tex]
So, we have:
[tex](f + g)(x) = 2x + 3 + x^2 - 4[/tex]
Collect Like Terms
[tex](f + g)(x) = x^2 +2x- 4+3[/tex]
[tex](f + g)(x) = x^2 +2x- 1[/tex]
