Question

Let (f(x) = 3x + 5) and (g(x) = 2x² - 8). Evaluate the expression shown below.

((f circ g)(-c))
What is the value of ((f circ g)(-c))?
a. (6c² - 22)
b. (-6c² + 22)
c. (6c² + 22)
d. (-6c² - 22)

Answer 1

After evaluating the function composition ((f o g)(-c)), the result is 6c² - 19. However, this result does not match any of the given options, suggesting there may be a typo in the question.

Step-by-step explanation:

To evaluate the expression ((f ∘ g)(-c)), we first need to understand the concept of function composition. The composition of two functions, (f ∘ g)(x), means you first apply g to x, and then apply f to the result of g(x). With our given functions f(x) = 3x + 5 and g(x) = 2x² - 8, we can find g(-c) first and then apply f to that result.

First we calculate g(-c) = 2(-c)² - 8 = 2c² - 8. Then we apply function f to this result: f(g(-c)) = f(2c² - 8) = 3(2c² - 8) + 5 = 6c² - 24 + 5 = 6c² - 19.

However, none of the options provided in the question match our result. There could be a typo in the question or the options provided.