Hi!

Considering the function

f(x) =

-x + x + 4 if x > -1

4 if x = -1

3 - x if x < -1

I was asked to show that the equation f(x) = -1 has a solution between 1 and 2. (Function was already determined to be continuous.)

For my solution:

f(x) = -(1)^3 + 1 + 4 = 4

f(x) = -(2)^3 + 2 + 4 = -2

Given that f(x) is a continuous function and f(2) < -1 < f(1) then by the intermediate value theorem there exists some number c such that f(x) = -1

Unfortuntely, I only recieved half credit for the answer. Is there something I missed? Was "f(2) < -1 < f(1)" the issue? Should I have manipulated my equations so that 0 would have been the center number?

(ex. f(x) -x^3 + x + 4 + 1 = 0 )

Any suggestions would be fantastic!

Thank you!