Question

Use f(x) = 2x − 4 and g(x) = 5 − x² to evaluate the expression.
(a) (f ∘ g)(−2)

Answer 1

To evaluate (f \circ g)(-2), we calculate g(-2) and then use that value as the input for f(x). We find g(-2) = 1, and then f(1) = -2. Hence, (f \circ g)(-2) is -2.

Step-by-step explanation:

To evaluate the expression (f \circ g)(-2), we need to first determine the output of g(x) when x is -2, and then use that result as the input for the function f(x).

Starting with g(x), we substitute x with -2:

g(-2) = 5 - (-2)^2 = 5 - 4 = 1

Now, we use the result as the input for f(x):

f(g(-2)) = f(1) = 2(1) - 4 = 2 - 4 = -2

Therefore, (f \circ g)(-2) = -2.

To evaluate the expression (f ∘ g)(-2), we need to substitute -2 into the function g(x) and then plug the result into the function f(x).

First, evaluate g(-2).

g(-2) = 5 - (-2)^2 = 5 - 4 = 1

Next, substitute the result into f(x).

f(1) = 2(1) - 4 = 2 - 4 = -2

Therefore, (f ∘ g)(-2) is equal to -2.