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Q4  Find the domain and the range of the real function f defined by f (x) = \sqrt{(x-1)}

Answers (1)

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Given function is 
f (x) = \sqrt{(x-1)}
We can clearly see that f(x) is only defined for the values of x ,  x\geq 1
Therefore,
The domain of the function f (x) = \sqrt{(x-1)}  is  [1,\infty)
Now, as
\Rightarrow x\geq 1
\Rightarrow x-1\geq 1-1
\Rightarrow x-1\geq 0
take square root on both sides
\Rightarrow \sqrt{x-1}\geq 0
\Rightarrow f(x)\geq 0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\because f(x)= \sqrt{x-1})
Therefore,
Range  of function f (x) = \sqrt{(x-1)}  is  [0,\infty)

Posted by

Gautam harsolia

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