Question

For the Piecewise below, Which of the following statements is true?

A) F(-1)>F(1)
B)F(-1) C)F(-1)=F(1)
D) The function is not defined at both F(-1) and F(1).

Answer 1

Answer: f(-1) > f(1) which is choice A

Step-by-step explanation

Function f(x) is composed of 3 helper functions. Those are:

• g(x) = (x+3)^2 - 1
• h(x) = -x
• k(x) = (5/2)*log(2, -x+4) - 1

The f(x) function will change its identity based on what the x input is.

• If -5 ≤ x ≤ -1, then f(x) = g(x)
• If -1 < x ≤ 1, then f(x) = h(x)
• If 1 < x ≤ 4, then f(x) = k(x)

The input x = -1 corresponds to the first piece g(x)

g(x) = (x+3)^2 - 1

g(-1) = (-1+3)^2 - 1

g(-1) = 3

Therefore f(-1) = 3

Meanwhile, the input x = 1 is for the second piece h(x).

h(x) = -x

h(1) = -1

Therefore f(1) = -1

We conclude that f(-1) > f(1) since 3 > -1 is the case.