Question

find the domain and range of f(x) = 1/√x|x|​

Answer 1

Answer:

The given real function is f(x)=

x−1

It can be seen that

x−1

is defined for (x−1)≥0

i.e., f(x)=

(x−1)

is defined for x≥1

Therefore the domain of f is the set of all real numbers greater than or equal to 1 i.e.,

the domain of f =[1,∞)

As x≥1

⇒(x−1)≥0

⇒

x−1

≥0

f(x)≥0

Therefore the range of f is the set of all real numbers greater than or equal to 0

i.e., the range of f =[0,∞)