Question

Determine the value of f (�3) for the function f of x is equal to the piecewise function x cubed plus 18 times x squared plus 104 times x plus 192 for x is less than negative 3 and the function quantity 3 times x plus 9 end quantity over the quantity x cubed plus 4 times x squared plus x minus 6 end quantity for negative 3 is less than or equal to x is less than 3 and the function square root of the quantity x squared minus 9 end quantity for x is greater than or equal to 3 period a 0 b undefined c 3 over 8 d 15

Answer 1

The value of f(-3) for the given function is undefined.

Step-by-step explanation:

The function f(x) is given as a piecewise function:

For x < -3, f(x) = x³ + 18x² + 104x + 192

For -3 ≤ x < 3, f(x) = (3x + 9) / (x³ + 4x² + x - 6)

For x ≥ 3, f(x) = √(x² - 9)

To determine the value of f(-3), we need to consider the second piece of the piecewise function. Substituting x = -3 into the function:

f(-3) = (3(-3) + 9) / ((-3)³ + 4(-3)² + (-3) - 6)

Simplifying further:

f(-3) = 0 / 0

The value of f(-3) is undefined.

Answer 2

By using the piecewise function, the output values for f(-3) include the following; a. 0.

In Mathematics and Euclidean Geometry, a piecewise-defined function is a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains.

Since the value of x is -3, the output value of this piecewise-defined function can be calculated by using the second piecewise-defined function over the interval -3 ≤ x < 3 as follows;

`f(x)=(3x+9)/(x^3-4x^(2) +x-6) \\\\f(-3)=(3(-3)+9)/((-3)^3-4(-3)^(2) +(-3)-6)\\\\f(-3)=(-9+9)/(-27-4(9) -3-6)\\\\f(-3)=(0)/(-27-36 -3-6)\\\\f(-3)=(0)/(-72)`

f(-3) = 0

Complete Question:

Determine the value of f(-3) for the function.

a. 0

b. undefined

c. 3/8

d. 15