Question

Consider the function

{8x-x^2 for x is less than or equal to 8
x^2+3 for x>8}

what is f(8)?

Answer 1

f(x) = 8x-x^2 only if x is equal to 8 or less than 8
OR
f(x) = x^2+3 only if x > 8

We can only pick one of the two paths. The function f(x) can't be both at the same time. In the case of computing f(8) we have the input x = 8. It won't fit the bottom piece as x > 8 is false when x = 8. The inequality 8 > 8 is false

So instead we pick the top piece

x = 8 ----> so "x is less than or equal to 8" is true
f(x) = 8x - x^2
f(8) = 8*8 - 8^2
f(8) = 64 - 64
f(8) = 0

The final answer is 0