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

Oct 31, 2015

Domain: $x \in \mathbb{R}$
Range: $F \left(x\right) \le 1 , \in \mathbb{R}$

#### Explanation:

$F \left(x\right) = 1 - {x}^{2}$ is defined for all Real values of $x$ and therefore the domain is all Real values ($\mathbb{R}$)

${x}^{2}$ has a minimum value of $0$ (for $x \in \mathbb{R}$)
therefore
$- {x}^{2}$ has a maximum value of $0$
and
$- {x}^{2} + 1 = 1 - {x}^{2}$ has a maximum value of $1$.

Therefore $F \left(x\right)$ has a maximum value of $1$
and the range of $F \left(x\right)$ is $\le 1$