What is the range of y absolute value fx if fx x2 And can y

What is the range of y= absolute value f(x) if f(x) = -x^2? And can you explain how you got the answer? Thanks

Solution

f(x)=-x^2

before commenting about the range of this firstly check its domain

now we can see that there is not a single point where the function is not defined

hence the domain is all real

now as x² is always positive whether x is +ve or -ve

hence

-x² is always negaive which is our function

hence

f(x)=-x² is alwayys negative

hence its range is (-infinnity, 0]