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The domain of the function f(x) = \frac{\sqrt{x - 1{x+1} is the
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16 Aug 2023, 06:00
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The domain of the function \(f(x) = \frac{\sqrt{x - 1} }{x+1}\) is the set of all real numbers that are
A. greater than 1
B. greater than or equal to 1
C. not equal to -1
D. less than or equal to 1
E. less than 1
A. greater than 1
B. greater than or equal to 1
C. not equal to -1
D. less than or equal to 1
E. less than 1
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Re: The domain of the function f(x) = \frac{\sqrt{x - 1{x+1} is the
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16 Aug 2023, 06:45
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Bunuel wrote:
The domain of the function \(f(x) = \frac{\sqrt{x - 1} }{x+1}\) is the set of all real numbers that are
A. greater than 1
B. greater than or equal to 1
C. not equal to -1
D. less than or equal to 1
E. less than 1
A. greater than 1
B. greater than or equal to 1
C. not equal to -1
D. less than or equal to 1
E. less than 1
We have to ensure the below constraints are met -
1) The value under the square root should always be non-negative.
\(\sqrt{x - 1}\)
\(x - 1 \geq 0\)
\(x \geq 1\)
2) The value of the denominator should not be zero
\(x + 1 \neq 0\)
\(x \neq -1\)
Combining information from both the constraints
\(x \geq 1\)
Option B
General Discussion
Re: The domain of the function f(x) = \frac{\sqrt{x - 1{x+1} is the
[#permalink]
16 Aug 2023, 09:20
f(x) = [(x-1)^0.5]/x+1
The domain is defined as the value of x that can be used in the function so that f(x) remains real,
here, f(x) has 2 parts => In the numerator, [(x-1)^0.5], to be real (x-1) should be greater than or equal to zero which gives, x E [1, infinity )
In the denominator, x+1, to be real (x+1) not be equal to zero which gives, xE [-1]
Taking final values, we get x E [1, infinity ) i.e. x should be equal to or greater than zero
Hence B
The domain is defined as the value of x that can be used in the function so that f(x) remains real,
here, f(x) has 2 parts => In the numerator, [(x-1)^0.5], to be real (x-1) should be greater than or equal to zero which gives, x E [1, infinity )
In the denominator, x+1, to be real (x+1) not be equal to zero which gives, x
Taking final values, we get x E [1, infinity ) i.e. x should be equal to or greater than zero
Hence B