Functions
A function f: R → R is defined by f(x) = ax + b. If f(1) = 5 and f(3) = 13, then f(5) equals
Select the correct option:
Solution
21
- Create Equations:
- f(1)=a+b=5
- f(3)=3a+b=13
- Solve System: Subtract the first from the second:
- (3a+b)−(a+b)=13−5⟹2a=8⟹a=4.
- Find 'b': From a+b=5⟹4+b=5⟹b=1.
- Function Rule: f(x)=4x+1.
- Evaluate at x=5: f(5)=4(5)+1=21.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- functions
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
21
- Create Equations:
- f(1)=a+b=5
- f(3)=3a+b=13
- Solve System: Subtract the first from the second:
- (3a+b)−(a+b)=13−5⟹2a=8⟹a=4.
- Find 'b': From a+b=5⟹4+b=5⟹b=1.
- Function Rule: f(x)=4x+1.
- Evaluate at x=5: f(5)=4(5)+1=21.
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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