Consider the piecewise function f(x)= {x^2-5, x ≤ -1. {-2x+3, x>-1 Determine the value of f(-5) + f(-6)

Answer 1

A piecewise function is a function that behaves differently depending on the value of x.

In this problem, when x is less than or equal to -1 then f(x) = x² - 5.

When x is greater than -1 then f(x) = -2x +3.

To determine the value of f(-5), we can plug -5 into the piece of the function that fits the description. In this case, -5 and -6 are both less than -1 so we can use the same "piece" :

f(-5) = (-5)² -5 = 25 - 5 = 20.

f(-6) = (-6)² -5 = 36 - 5 = 31.

Hope this helps!

Answer 2

Since -5 and -6 are both less than -1, we can use the x^2 - 5 part of the piecewise function to find the value of f(-5) and f(-6)

f(-5) = (-5)^2 - 5 = 25 - 5 = 20

f(-6) = (-6)^2 - 5 = 36 - 5 = 31

So, f(-5) + f(-6) = 20 + 31 = 51