The domain and range of the function f(x) and g(x) are same.
- A domain of a function refers to "all the values" that go into a function
- The domain of a function is the set of all possible inputs for the function.
- The range of a function is the set of all its outputs.
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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