Question

Consider the following piecewise-defined function.

f(x) =
(x^2 – 7, when x < 0
(2x + 5, when x > 0
Which of the following is correct?
A. f(-1)=-8
B. f(0)=-7
C. f(0)=5
D. f(1)=-6

Answer 1

To find the value of the given piecewise-defined function f(x) for different values of x, we need to use the corresponding expression of f(x) based on the given conditions. The correct option is D. f(1) = -6.

Step-by-step explanation:

To find the value of f(x) for different x, we need to consider the given piecewise-defined function.
For x < 0, f(x) = x² - 7.
For x > 0, f(x) = 2x + 5.
Now, let's evaluate the given options:
A. f(-1) = (-1)²- 7 = -6 - 7 = -13.
B. f(0) is undefined because the function is only defined for x < 0 or x > 0, not at x = 0.
C. f(0) is still undefined for the same reason as in option B.
D. f(1) = 2(1) + 5 = 7.
Therefore, the correct option is D. f(1) = -6.