Composition Of Functions
Let f(x) = 2x + 3 and g(x) = x^2 - 1 be real functions; the value of the composite (f ∘ g)(2) minus (g ∘ f)(0) equals which number?
Select the correct option:
Solution
1
Function composition applies one function to the output of another, with (f ∘ g)(x) meaning f(g(x)), a foundational operation in JEE Advanced function problems. Compute (f ∘ g)(2): first g(2) = 2^2 - 1 = 3, then f(3) = 2·3 + 3 = 9. Compute (g ∘ f)(0): first f(0) = 2·0 + 3 = 3, then g(3) = 3^2 - 1 = 8. The required difference is 9 - 8 = 1. Order matters because composition is generally non-commutative, which this problem deliberately tests. Option 9 reports only the first composite, ignoring the subtraction. Option -1 reverses the order of subtraction. Option 5 results from mistakenly computing g(f(0)) as 2·3 - 1. Hence the answer is 1. Plausibility check: since f ∘ g and g ∘ f differ here (9 versus 8), their near-equality confirms the expected non-commutativity of composition without the functions being inverses, consistent with the standard composition pattern.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- composition of functions
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
1
Function composition applies one function to the output of another, with (f ∘ g)(x) meaning f(g(x)), a foundational operation in JEE Advanced function problems. Compute (f ∘ g)(2): first g(2) = 2^2 - 1 = 3, then f(3) = 2·3 + 3 = 9. Compute (g ∘ f)(0): first f(0) = 2·0 + 3 = 3, then g(3) = 3^2 - 1 = 8. The required difference is 9 - 8 = 1. Order matters because composition is generally non-commutative, which this problem deliberately tests. Option 9 reports only the first composite, ignoring the subtraction. Option -1 reverses the order of subtraction. Option 5 results from mistakenly computing g(f(0)) as 2·3 - 1. Hence the answer is 1. Plausibility check: since f ∘ g and g ∘ f differ here (9 versus 8), their near-equality confirms the expected non-commutativity of composition without the functions being inverses, consistent with the standard composition pattern.
This easy difficulty mathematics question is from the chapter sets, relations and functions, covering the topic of composition of functions. It appeared in the 2025 exam.
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