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If f : [1,∞) [2,∞) is given by f(x) = x +1/x , then f –1(x) is equal to
- a)x + √x2 -4/2
- b)x/1 -x2
- c)x - √x2 -4/2
- d)1 + √x2 -4
Correct answer is option 'A'. Can you explain this answer?
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If f : [1,∞) [2,∞) is given by f(x) = x +1/x , then f &nda...
Understanding the Function f(x)
The function f is defined as:
- f(x) = x + 1/x, where x is in the interval [1, ∞).
Finding the Inverse Function f-1(x)
To find the inverse of f, we start with the equation:
- y = x + 1/x
Rearranging it gives:
- y - x = 1/x
Multiplying through by x yields:
- yx - x^2 = 1
This can be rewritten as:
- x^2 - yx + 1 = 0
Applying the Quadratic Formula
This equation is a quadratic in terms of x. The general form is:
- ax^2 + bx + c = 0, where a = 1, b = -y, and c = 1.
Using the quadratic formula:
- x = [ -b ± √(b² - 4ac) ] / 2a
Substituting the values gives:
- x = [ y ± √(y² - 4) ] / 2
Selecting the Correct Root
Since the domain of f is [1, ∞), we need the positive root, leading to:
- x = [ y + √(y² - 4) ] / 2
Thus, we can express the inverse function as:
- f-1(x) = [ x + √(x² - 4) ] / 2
Final Answer
The correct option is:
- a) x + √(x² - 4) / 2
This confirms that option 'A' is indeed the right answer for f-1(x).
The function f is defined as:
- f(x) = x + 1/x, where x is in the interval [1, ∞).
Finding the Inverse Function f-1(x)
To find the inverse of f, we start with the equation:
- y = x + 1/x
Rearranging it gives:
- y - x = 1/x
Multiplying through by x yields:
- yx - x^2 = 1
This can be rewritten as:
- x^2 - yx + 1 = 0
Applying the Quadratic Formula
This equation is a quadratic in terms of x. The general form is:
- ax^2 + bx + c = 0, where a = 1, b = -y, and c = 1.
Using the quadratic formula:
- x = [ -b ± √(b² - 4ac) ] / 2a
Substituting the values gives:
- x = [ y ± √(y² - 4) ] / 2
Selecting the Correct Root
Since the domain of f is [1, ∞), we need the positive root, leading to:
- x = [ y + √(y² - 4) ] / 2
Thus, we can express the inverse function as:
- f-1(x) = [ x + √(x² - 4) ] / 2
Final Answer
The correct option is:
- a) x + √(x² - 4) / 2
This confirms that option 'A' is indeed the right answer for f-1(x).
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Question Description
If f : [1,∞) [2,∞) is given by f(x) = x +1/x , then f –1(x) is equal toa)x + √x2-4/2b)x/1 -x2c)x - √x2-4/2d)1 + √x2-4Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If f : [1,∞) [2,∞) is given by f(x) = x +1/x , then f –1(x) is equal toa)x + √x2-4/2b)x/1 -x2c)x - √x2-4/2d)1 + √x2-4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If f : [1,∞) [2,∞) is given by f(x) = x +1/x , then f –1(x) is equal toa)x + √x2-4/2b)x/1 -x2c)x - √x2-4/2d)1 + √x2-4Correct answer is option 'A'. Can you explain this answer?.
If f : [1,∞) [2,∞) is given by f(x) = x +1/x , then f –1(x) is equal toa)x + √x2-4/2b)x/1 -x2c)x - √x2-4/2d)1 + √x2-4Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If f : [1,∞) [2,∞) is given by f(x) = x +1/x , then f –1(x) is equal toa)x + √x2-4/2b)x/1 -x2c)x - √x2-4/2d)1 + √x2-4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If f : [1,∞) [2,∞) is given by f(x) = x +1/x , then f –1(x) is equal toa)x + √x2-4/2b)x/1 -x2c)x - √x2-4/2d)1 + √x2-4Correct answer is option 'A'. Can you explain this answer?.
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