How do you find the domain and range of $f(x) = sqrt(x+3)$ ?

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Answer 1 · 2017-09-11T23:03:12

See below.

This is for positive roots, since $sqrt(a)$ usually implies positive roots.

For real numbers $x + 3 >= 0 => x >= -3$

So domain is:

${x in RR | x>= -3 }$

Minimum value of range is $0$ when $x = -3$

$sqrt( -3 + 3 ) = 0$

As $x -> oo$

$sqrt(x + 3) -> oo$

so range is:

${y in RR | y >= 0 }$

How do you find the domain and range of f(x) = sqrt(x+3)f(x) = sqrt(x+3)?