1.

Find the domain and Range of the function f (x) = 1/√x−5 .

Answer»

Given: f (x) = 1/√x−5 .

To find: the domain and range of function

Explanation: So, the domain of a function consists of all the first elements of all the ordered pairs, i.e., x, so we have to find the values of x to get the required domain

Given,

f (x) = 1/√x−5 .

Now for real value of

x-5≠0 and x-5>0

⇒ x≠5 and x>5

Hence the domain of f = (5, ∞)

And the range of a function consists of all the second elements of all the ordered pairs, i.e., f(x), so we have to find the values of f(x) to get the required range

Now we know for this function

x-5>0

taking square root on both sides, we get

√x−5 > 0

Or

1/√x−5 > 0

Or

f(x)>0

⇒ f(x)∈(0, ∞)

Hence the range of f = (0, ∞)


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