Answer:
[tex]A.\ (f+g)(x) =2x^2+11x-41\\\\ (f+g)(3) =10\\\\\\ B.\ (f-g)(x)=3x^3-x^2-72x+46\\\\ (f-g)(-5)=6[/tex]
Step-by-step explanation:
A. Knowing that the functions are:
[tex]f(x) = x^2 + 16x - 24\\\\g(x) = x^2 - 5x - 17[/tex]
You need to add them in order to find [tex](f+g)(x)[/tex]. Then, you get:
[tex](f+g)(x) = x^2 + 16x - 24+x^2 - 5x - 17\\\\(f+g)(x) =2x^2+11x-41[/tex]
To find:
[tex](f+g)(3)[/tex]
Substitute [tex]x=3[/tex] into [tex](f+g)(x)[/tex] and evaluate.
Then, this is:
[tex](f+g)(3) =2(3)^2+11(3)-41\\\\(f+g)(3) =10[/tex]
B. The functions f(x) and g(x) are:
[tex]f(x) =4x^3 - x^2 - 68x + 35\\\\g(x) = x^3 + 4x - 11[/tex]
You need to subtract them in order to find [tex](f-g)(x)[/tex]:
[tex](f-g)(x) = 4x^3 - x^2 - 68x + 35-(x^3 + 4x - 11)\\\\(f-g)(x) =4x^3 - x^2 - 68x + 35-x^3 -4x +11\\\\(f-g)(x)=3x^3-x^2-72x+46[/tex]
To find:
[tex](f-g)(-5)[/tex]
Substitute [tex]x=-5[/tex] into [tex](f-g)(x)[/tex] and evaluate.
Then, this is:
[tex](f-g)(-5)=3(-5)^3-(-5)^2-72(-5)+46\\\\(f-g)(-5)=6[/tex]
