Question

What is the domain and range of `f(x)=1-x^2`?

Answer 1

Domain : `x| RR`. In interval notation: `(-oo, oo)`
Range: `f(x) <=1`. In interval notation: `(-oo, 1]`

Explanation:

`f(x) = 1-x^2 or f(x) = -x^2 +1 or f(x) = -(x-0)^2+1`

This is a quadratic equation , i.e parabola openning downwards ,

with vertex at `0,1` , Maximum point , `f(x)=1`

Domain : `x` may be any real number i.e `x| RR`. In interval notation `(-oo, oo)`

Range: `f(x) <=1`. In interval notation `(-oo, 1]` graph{-x^2+1 [-10, 10, -5, 5]} [Ans]