Answer:
a) -1
b) -11
c) -6
d) -10/21
Step-by-step explanation:
We have that
[tex]f(x) = 3x - 5[/tex]
[tex]g(x) = 4 - x^{2}[/tex]
So
[tex](f + g)(x) = 3x - 5 + 4 - x^{2} = -x^{2} + 3x - 1[/tex]
[tex](f-g)(x) = 3x - 5 - 4 + x^{2} = x^{2} + 3x - 9[/tex]
[tex](fg)(x) = (3x - 5)(4 - x^{2})[/tex]
[tex]\frac{f}{g}(x) = \frac{3x - 5}{4 - x^{2})[/tex]
(a) (f+g)(3)
[tex](f + g)(x) = 3x - 5 + 4 - x^{2} = -x^{2} + 3x - 1[/tex]
We replace x by 3. So
[tex](f+g)(3) = -3^{2} + 3*3 - 1 = -1[/tex]
(b) (f-g)(- 2)
[tex](f-g)(x) = 3x - 5 - 4 + x^{2} = x^{2} + 3x - 9[/tex]
We replace x by -2. So
[tex](f-g)(-2) = (-2)^{2} + 3(-2) - 9 = -11[/tex]
(c) (fg)(1)
[tex](fg)(x) = (3x - 5)(4 - x^{2})[/tex]
We replace x by 1. So
[tex](fg)(1) = (3*1 - 5)(4 - (1)^{2}) = -6[/tex]
(d) (f/g)(5)
[tex]\frac{f}{g}(x) = \frac{3x - 5}{4 - x^{2})[/tex]
We replace x by 5. So
[tex]\frac{f}{g}(x) = \frac{3*5 - 5}{4 - (5)^{2}) = -\frac{10}{21}[/tex]
