Answer:
See Below.
Step-by-step explanation:
We are given the two functions:
[tex]\displaystyle f(x) = x^2 + 5x \text{ and } g(x) = 4x - 7[/tex]
9)
We want to find:
[tex]f(x) + g(x)[/tex]
Substitute:
[tex]\displaystyle = (x^2 + 5x) + (4x - 7)[/tex]
And combine like terms. Hence:
[tex]f(x) + g(x) = x^2 + 9x - 7[/tex]
10)
We want to find:
[tex]f(x) - g(x)[/tex]
Substitute:
[tex]= (x^2 + 5x) - (4x - 7)[/tex]
Distribute:
[tex]= (x^2 + 5x) + (-4x +7)[/tex]
And combine like terms. Hence:
[tex]f(x) - g(x) = x^2 +x +7[/tex]
11)
We want to find:
[tex]\displaystyle f(x) \cdot g(x)[/tex]
Substitute:
[tex]\displaystyle = (x^2 + 5x)(4x-7)[/tex]
Expand:
[tex]\displaystyle = 4x(x^2 + 5x) - 7(x^2 + 5x) \\ \\ = (4x^3 + 20x^2) + (-7x^2 -35x) \\ \\ = 4x^3 + 13x^2 - 35x[/tex]
Hence:
[tex]\displaystyle f(x) \cdot g(x) = 4x^3 + 13x^2 - 35x[/tex]
12)
We want to find:
[tex]g(x) - f(x)[/tex]
Substitute:
[tex]= (4x -7) - (x^2 + 5x)[/tex]
Distribute:
[tex]= (4x-7) + (-x^2 - 5x)[/tex]
And combine like terms. Hence:
[tex]\displaystyle g(x) - f(x) = -x^2 -x -7[/tex]
