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

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Answer 1 · 2015-10-31T10:30:26

Domain: $x in RR$
Range: $F(x) <= 1, in RR$

$F(x) = 1-x^2$ is defined for all Real values of $x$ and therefore the domain is all Real values ( $RR$ )

$x^2$ has a minimum value of $0$ (for $x in RR$ )
therefore
$-x^2$ has a maximum value of $0$
and
$-x^2+1 = 1-x^2$ has a maximum value of $1$ .

Therefore $F(x)$ has a maximum value of $1$
and the range of $F(x)$ is $<= 1$

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