Question

F(x)=2x²+19x+35 and g(x)=-x-7

Which answer choices are true? Select all that apply.
a. f-g=2x²+20x+42
b. f/g=-2x-5
c. g(f(-3))=-11
d. g(x): As x ➔ [infinity], y ➔ -[infinity]

Answer 1

To solve this question, we perform operations using the given functions f(x) and g(x) and determine which answer choices are true.

Step-by-step explanation:

To solve this question, we need to perform a few operations using the given functions f(x) and g(x).

1. To find f - g, we subtract the function g(x) from f(x) term by term:
   f - g = (2x² + 19x + 35) - (-x - 7) = 2x² + 20x + 42
   So, option a is true.
2. To find f/g, we divide f(x) by g(x):
   f/g = (2x² + 19x + 35) / (-x - 7) = -2x - 5
   So, option b is true.
3. To find g(f(-3)), we substitute -3 for x in f(x) and then substitute the result in g(x):
   g(f(-3)) = g(2(-3)² + 19(-3) + 35) = g(-9 + (-57) + 35) = g(-31) = -(-31) - 7 = 24
   So, option c is false.
4. As x approaches infinity, the y value of g(x) approaches negative infinity:
   g(x): as x ➔ ∞, y ➔ -∞
   So, option d is true.