The domain and range of the function f(x) and g(x) are same.
Domain of function f(x)
The argument inside the square root function must be positive for the square root to be defined.
[tex]\sqrt{x-1}[/tex] >0
On squaring , we get
x-1 > 0
on adding 1 both sides we get
x>1
domain of f(x) is x>1
since f(x) is square root function it is always positive hence the range of f(x) is {0,infinity}
Domain of function g(x)
The argument inside the square root function must be positive for the square root to be defined.
[tex]\sqrt{x}[/tex]-1>0
on adding 1 both sides we get
[tex]\sqrt{x}[/tex] > 1
On squaring , we get
x > 1
domain of g(x) is x> 1
g(x) it is always positive hence the range of f(x) is {0,infinity}
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