How do you find the domain and range for $f(x)=sqrt( 3-8x)$ ?

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Answer 1 · 2017-05-17T05:12:26

The domain is $x in (-oo, 3/8]$
The range is $f(x) in [0,+oo)$

$f(x)=sqrt(3-8x)$

What's under the square root sign is $>=0$

Therefore,

$3-8x>=0$

$8x<=3$

$x<=3/8$

so,

The domain of $f(x)$ is $x in (-oo, 3/8]$

when $x=3/8$ , $f(3/8)=0$

and when $x=-oo$ , $f(-oo)=+oo$

So the range is $f(x) in [0,+oo)$

How do you find the domain and range for f(x)=sqrt( 3-8x)f(x)=sqrt( 3-8x)?