Question

Find f(8) for this piecewise -defined function. f(x)={(8x+2 if x<-3),(-3x+8 if -3<=x<2),(-4x-2 if x>=2):} Write your answer as an integer or as a fraction in simplest form. f(8)

Answer 1

To find f(8), substitute x = 8 into the last piece of the function, f(x) = -4x - 2. Therefore, the value of f(8) is -34.

Step-by-step explanation:

The given piecewise-defined function is:
f(x) = {8x + 2 if x < -3, -3x + 8 if -3 ≤ x < 2, -4x - 2 if x ≥ 2}
To find f(8), we need to determine which piece of the function applies to x = 8. Since x ≥ 2, the last piece of the function, f(x) = -4x - 2, applies.

Substituting x = 8 into f(x) = -4x - 2:
f(8) = -4(8) - 2
f(8) = -32 - 2
f(8) = -34

Therefore, the value of f(8) is -34.