Question

Supposed f(x) = 2x+5 and g(x) = -1/3x + 2. Find Each Value for -2f(x+1) and f(-2)/g(f(-2)+1).

a. -20, -0.15
b. -15, 0.20
c. -10, -0.10
d. -5, 0.25

Answer 1

After step-by-step evaluation of the given functions and expressions, the values obtained are -14 and 0.75, which do not match any of the provided answer choices (a, b, c, d).

Step-by-step explanation:

The student is asked to find the values of expressions involving compositions and combinations of two functions f(x) and g(x), given by f(x) = 2x + 5 and g(x) = -1/3x + 2. The expressions to be evaluated are -2f(x+1) and f(-2)/g(f(-2)+1).

Let's evaluate each expression step by step:

1. First, we calculate f(x+1) = 2(x+1) + 5 = 2x + 7.
2. Then, multiplying by -2 gives us -2f(x+1) = -2(2x + 7) = -4x - 14. When x = 0, this simplifies to -14.
3. Next, we evaluate f(-2) = 2(-2) + 5 = -4 + 5 = 1.
4. To find f(-2)+1, simply add 1 to previous result, yielding 2.
5. Then, we evaluate g(f(-2)+1) = g(2) = -1/3(2) + 2 = -2/3 + 2 = 4/3.
6. Finally, the ratio f(-2)/g(f(-2)+1) = 1/(4/3) = 3/4 = 0.75.

Therefore, the values of the expressions are -14 and 0.75, which does not match any of the given options (a, b, c, d).