How do you find the domain and range of #1/sqrt(8-t)#?

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Answer 1 · 2017-12-01T00:59:42

Domain: All #x# values#< 8#; #\quad[\infty,8)#

Range: All #y# values#>0#; #\quad(0,\infty]#

The domain is simply the values #x#, or in this case #t#, can have that will make the function defined.

For the above function, dividing by #0# will be undefined, so #t\ne 8#.

We can express that in interval notation as #[\infty,8)#, which means the domain is all values of #t# less than #8#.

As for the range, we can plot the graph and find it from that.

Desmos

We can see the graph starts just above #0#, and continues toward #\infty# upward.

So we can express the range as #(0,\infty]#, meaning all #y>0#.