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Answered

  1. If f(x) = 8 – 10x and g(x) = 5x + 4, what is the value of (fg)(–2)?

A–196
B–168
C22
D78

  1. If f(x) is an odd function and the graph of f(x) includes points in Quadrant IV, which statement about the graph of f(x) must be true?

AIt includes points in Quadrant I.
BIt includes points in Quadrant II.
CIt does not include points in Quadrant I.
DIt does not include points in Quadrant II.

  1. If f(x) = 3x2 + 1 and g(x) = 1 – x, what is the value of (f – g)(2)?

A12
B14
C36
D38

Verified Answer :

metchelle
  1. f(x) = 8 - 10xg(x) = 5x + 4
    (fg)(x) = (8 - 10x)(5x + 4)(fg)(x) = 40x + 32 - 50x^2 - 40x(fg)(x) = 32 - 50x^2
    (fg)(-2) = 32 - 50(-2)^2(fg)(-2) = 32 - 200(fg)(-2) = -168
    2. Signs are inverted. Since, Q4 = (x , -y)Therefore Q? = (-x , y), which belongs to Quadrant 2.
    b) It includes points in Quadrant II
    3. f(x) = 3x^2 + 1g(x) = 1 - x
    (f - g)(x) = 3x^2 + 1 - (1 - x)(f - g)(x) = 3x^2 + 1 - 1 + x(f - g)(x) = 3x^2 + x(f - g)(2) = 3(2)^2 + 2(f - g)(2) = 14

The answers are as follows:

  1. If f(x) = 8 - 10x and g(x) = 5x + 4, then the value of (f g)(-2) = -168. So, option b is correct.
  2. If f(x) is an odd function and its graph lies in the 4th quadrant, then statement (b) is true. I.e., it includes points in quadrant 2.
  3. If f(x) = 3x² + 1 and g(x) = 1 - x, the value of (f - g)(2) = 14. So, option b is correct.

What are the operations on functions?

The basic operations like addition, subtraction, multiplication and division on functions are as follows:

Addition: (f + g)(x) = f(x) + g(x)

Subtraction: (f - g)x = f(x) - g(x)

Multiplication: (f g)x = f(x). g(x)

Division: (f/g)x = f(x)/g(x)

Calculation:

1) f(x) = 8 – 10x and g(x) = 5x + 4,

Then,

(f g) (-2) = f(-2) × g(-2)

             = (8 - 10(-2)) × (5(-2) + 4)

             = 28 × (-6)

             = -168

So, option b is correct.

2) f(x) is an odd function, so the graph of f(x) includes points in Quadrant IV

Since it is odd function,

f(-x) = - f(x)

So, for the negative values of x, the function f(x) lies in the second qudrant.

Thus, option b is correct.

3) If f(x) = 3x² + 1 and g(x) = 1 – x,

Then,

(f – g)(2) = f(2) -g(2)

              = (3(2)²+1) - (1 - 2)

              = 13 + 1

              = 14

So, option b is correct.

Learn more about functions here:

https://brainly.com/question/4545383

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