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)#