use f(x)= { x^2 +5 if x ≤ 1
{ -x^2+4x+3 if x>1
to find the answers to the following:
1. f(2)
2. f(4)-f(-2)
To find the answers to the given questions using the function f(x), follow these steps:
1. Find f(2):
- Since 2 is greater than 1, we need to use the second part of the function: -x^2 + 4x + 3.
- Plug in x = 2 into the second part of the function:
f(2) = -(2^2) + 4(2) + 3
f(2) = -4 + 8 + 3
f(2) = 7
Therefore, f(2) = 7.
2. Find f(4) - f(-2):
- To find f(4), we'll use the second part of the function since 4 is greater than 1: -x^2 + 4x + 3.
- Plug in x = 4 into the second part of the function:
f(4) = -(4^2) + 4(4) + 3
f(4) = -16 + 16 + 3
f(4) = 3
- To find f(-2), we'll use the first part of the function since -2 is less than or equal to 1: x^2 + 5.
- Plug in x = -2 into the first part of the function:
f(-2) = (-2^2) + 5
f(-2) = 4 + 5
f(-2) = 9
- Now subtract f(-2) from f(4):
f(4) - f(-2) = 3 - 9
f(4) - f(-2) = -6
Therefore, f(4) - f(-2) = -6.