1 Answer

Hjblok · Answer 1 · 2021-08-21T08:44:30+0000

Answer:

a) -1

b) -11

c) -6

d) -10/21

Explanation:

We have that

f(x) = 3x - 5

g(x) = 4 - x^(2)

So

(f + g)(x) = 3x - 5 + 4 - x^(2) = -x^(2) + 3x - 1

(f-g)(x) = 3x - 5 - 4 + x^(2) = x^(2) + 3x - 9

(fg)(x) = (3x - 5)(4 - x^(2))

$(f)/(g)(x) = \frac{3x - 5}{4 - x^(2))$

(a) (f+g)(3)

(f + g)(x) = 3x - 5 + 4 - x^(2) = -x^(2) + 3x - 1

We replace x by 3. So

(f+g)(3) = -3^(2) + 3*3 - 1 = -1

(b) (f-g)(- 2)

(f-g)(x) = 3x - 5 - 4 + x^(2) = x^(2) + 3x - 9

We replace x by -2. So

(f-g)(-2) = (-2)^(2) + 3(-2) - 9 = -11

(c) (fg)(1)

(fg)(x) = (3x - 5)(4 - x^(2))

We replace x by 1. So

(fg)(1) = (3*1 - 5)(4 - (1)^(2)) = -6

(d) (f/g)(5)

$(f)/(g)(x) = \frac{3x - 5}{4 - x^(2))$

We replace x by 5. So

$(f)/(g)(x) = \frac{3*5 - 5}{4 - (5)^(2)) = -(10)/(21)$

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