Question

Let f(x) = x² - 1, g(x) = 1/2x, find (g * f)(-1):
a) -2
b) -1
c) 0
d) 1

Answer 1

To find the composition (g*f)(-1), we calculate f(-1) and then apply g to that result. We find f(-1) equals 0, and then applying g(0) equals 0. Hence, the composition (g*f)(-1) equals 0, not 1.

Step-by-step explanation:

The question asks us to find the composition of the functions f(x) and g(x), denoted as (g * f)(-1). The function f(x) = x² - 1 and g(x) = ½x. To find the composition (g * f)(x), we first apply the function f to x and then apply the function g to the result of f(x).

To find (g * f)(-1), we first need to find g(f(-1)).

Substitute -1 into f(x) = x² - 1:

f(-1) = (-1)² - 1 = 1 - 1 = 0.

Now, substitute f(-1) into g(x) = 1/2x:

g(f(-1)) = 1/2 * 0 = 0.

Therefore, (g * f)(-1) is equal to 0.

Let's start by finding f(-1):
f(-1) = (-1)² - 1 = 1 - 1 = 0.

Now, we will find g(f(-1)) by plugging the result of f(-1) into g(x):
g(f(-1)) = g(0) = ½ × 0 = 0.

Therefore, the value of the composition (g * f)(-1) is 0, which is different from the student's provided answer of 1.