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

May 24, 2017

Domain : $x | \mathbb{R}$. In interval notation: $\left(- \infty , \infty\right)$
Range: $f \left(x\right) \le 1$. In interval notation: $\left(- \infty , 1\right]$

#### Explanation:

$f \left(x\right) = 1 - {x}^{2} \mathmr{and} f \left(x\right) = - {x}^{2} + 1 \mathmr{and} f \left(x\right) = - {\left(x - 0\right)}^{2} + 1$

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

with vertex at $0 , 1$ , Maximum point , $f \left(x\right) = 1$

Domain : $x$ may be any real number i.e $x | \mathbb{R}$. In interval notation $\left(- \infty , \infty\right)$

Range: $f \left(x\right) \le 1$. In interval notation $\left(- \infty , 1\right]$ graph{-x^2+1 [-10, 10, -5, 5]} [Ans]