How do you find the domain and range of #y = sqrt(x^2 - 1)#?

1 Answer
Dec 2, 2017

Answer:

Range: #y>=0#
Domain: #x>=1# and #x<=-1#

Explanation:

We can first consider the range, rather simply, we must consider all the values that #y# can take on, but as we know #sqrt alpha >=0# ,#alpha in RR#, or in other words, the square root of a value can never be negative for #x in RR#, so hence #y>=0#

Now we can consider the domain, to what we can consider for what values of #x# yields and valid value of #y#, we know the valid values of #sqrt delta# is where #delta >=0#, so in this circumstance we must consider where #x^2-1 >=0# we can sketch to find the values:
graph{x^2-1 [-3.538, 3.572, -1.437, 2.118]}

we can evidently see that where #x^2-1 >= 0# is for #x>=1# and #x<=-1#

So hence the domain is; #x>=1 and x<=-1#