Question

Find the range:

Let f(x)=1/sqrt(x−5)

Answer 1

this is not quite correct mrb

Answer 2

woops, your right
ignore my last post

Answer 3

f(x) must be greater than 0, because you can get sqrt(x-5) arbitrarily close to 0

Answer 4

domain is (5, +infinity)

As the x-values get bigger without bound, the denominator follows, therefore the frac gets very close to 0, but it never equals it.

As the x-values get closer and closer to 5, from the right of 5, the denominator will get smaller and smaller approaching 0, so the fraction will go to +infinity.

Thus, the range is (0, +infinity)

Answer 5

the graph has whats know as a vertical asymptote at x=5 and a horizontal asymptote of y=0 (the x-axis). see attached graph