According to the image, the symmetry axis of the function is x= 1/2.

On [- 1, 1/2], the function is an increasing function with the range of [- 1, 5/4].

On [1/2, 1], this function is a decreasing function with the range of [1, 5/4].

∴ On [- 1, 1], the function range is [- 1, 5/4].

X∈[- 1, 1] does not exist, so f(x)=-2.