Functions
If f: [0, 1] → R is defined by f(x) = x³ - 6x² + 11x - 6 and g denotes the inverse of f on its range, then g'(0) equals
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Solution
1/2
- Inverse Derivative Rule: g′(y)=f′(x)1 where y=f(x).
- Identify x for y=0: Solve x3−6x2+11x−6=0.
- By inspection, x=1 gives 1−6+11−6=0. So f(1)=0.
- Derivative of f: f′(x)=3x2−12x+11.
- Evaluate at x=1: f′(1)=3(1)2−12(1)+11=2.
- Apply Rule: g′(0)=f′(1)1=21.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- functions
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
1/2
- Inverse Derivative Rule: g′(y)=f′(x)1 where y=f(x).
- Identify x for y=0: Solve x3−6x2+11x−6=0.
- By inspection, x=1 gives 1−6+11−6=0. So f(1)=0.
- Derivative of f: f′(x)=3x2−12x+11.
- Evaluate at x=1: f′(1)=3(1)2−12(1)+11=2.
- Apply Rule: g′(0)=f′(1)1=21.
This hard 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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