Functions
If f: R → R is defined by f(x) = 3x - 5, then f⁻¹(x) equals
Select the correct option:
Solution
(x + 5)/3
- Identify Inverse Method: To find the inverse of y=f(x), solve the equation for x in terms of y.
- Set up Equation: y=3x−5.
- Algebraic Manipulation:
- Add 5 to both sides: y+5=3x
- Divide by 3: x=3y+5.
- Final Step: Swap variables to express in x: f−1(x)=3x+5.
- Verification: f(f−1(x))=3(3x+5)−5=x+5−5=x.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- functions
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
(x + 5)/3
- Identify Inverse Method: To find the inverse of y=f(x), solve the equation for x in terms of y.
- Set up Equation: y=3x−5.
- Algebraic Manipulation:
- Add 5 to both sides: y+5=3x
- Divide by 3: x=3y+5.
- Final Step: Swap variables to express in x: f−1(x)=3x+5.
- Verification: f(f−1(x))=3(3x+5)−5=x+5−5=x.
This easy difficulty mathematics question is from the chapter sets, relations and functions, covering the topic of functions. It appeared in the 2025 exam.
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