Composition of Functions and Invertible Functions Quiz - CBSE Class 12 Mathematics

Free practice quiz: Composition of Functions and Invertible Functions (CBSE Class 12 Mathematics). 13 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 12 Mathematics practice quiz has 13 multiple-choice questions on Composition of Functions and Invertible Functions, and 13 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. If f(x) = 2x + 3 and g(x) = x - 2, find (f ∘ g)(x).

   1. 2x - 1
   2. 2x + 1
   3. 2x - 5
   4. 4x - 1
   Show answer

   Answer: A. 2x - 1

   The composition (f ∘ g)(x) means f(g(x)). Since g(x) = x - 2, substitute x - 2 into f(x): f(x) = 2(x - 2) + 3 = 2x - 4 + 3 = 2x - 1.

2. If f(x) = 5x + 7, find the inverse function f⁻¹(x).

   1. (x - 7)/5
   2. (x + 7)/5
   3. 5x + 7
   4. 5(x - 7)
   Show answer

   Answer: A. (x - 7)/5

   To find the inverse, swap x and y in the equation y = 5x + 7, giving x = 5y + 7. Solve for y: y = (x - 7)/5, so f⁻¹(x) = (x - 7)/5.

3. If h(x) = 4x + 8, what is the value of (h ∘ h⁻¹)(10)?

   1. 10
   2. 12
   3. 8
   4. 6
   Show answer

   Answer: A. 10

   The composition (h ∘ h⁻¹)(x) is equal to x, hence (h ∘ h⁻¹)(10) = 10.

4. Prove that f(x) = (2x + 3)/(3x + 5) is invertible.

   1. Yes, it is a bijection.
   2. No, it is not a bijection.
   3. Yes, it is injective but not surjective.
   4. No, it is surjective but not injective.
   Show answer

   Answer: A. Yes, it is a bijection.

   To prove that a function is invertible, it must be bijective. f(x) = (2x + 3)/(3x + 5) is both injective and surjective based on its domain, therefore it is a bijection.

5. Prove f(x) = log(x+1) is injective over the domain x > -1.

   1. It's injective because f(x) has a unique derivative.
   2. It is not injective because it is logarithmic.
   3. It is injective as it's strictly increasing.
   4. It is not injective because for x = -1
   Show answer

   Answer: C. It is injective as it's strictly increasing.

   The function f(x) = log(x+1) is strictly increasing for x > -1, implying that if x1 < x2 -> f(x1) < f(x2), meeting injective criteria definitively over given domain.

More questions in this quiz

Answers and explanations are in the full quiz.

1. If h(x) = 3x^2 - 6x + 2 and k(x) = x + 1, what is (k ∘ h)(x)?
2. Find (g ∘ f)(x) given f(x) = x² + 1 and g(x) = x + 3.
3. Find the inverse of the function g(x) = (x - 3)/7.
4. Determine if the function f(x) = x³ - 2 is invertible.
5. Is the function f(x) = x² bijective if defined over all real numbers?
6. If f and g are inverse functions, which property holds for any x in the domain?
7. Determine if the function h(x) = e^x is invertible.
8. Prove the function f(x) = x³ + 1 is invertible.

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