Set, Relations and FunctionsMTP Apr 21Question 1979 of 217
All Questions

If A={1,2,3,4}\displaystyle A = \{1,2,3,4\}, B={2,4,6,8}\displaystyle B = \{2,4,6,8\}, f:A→B\displaystyle f: A \to B then f−1\displaystyle f^{-1} is:

Options

A{(2,1),(4,2),(6,3),(8,4)}\displaystyle \{(2,1), (4,2), (6,3), (8,4)\}
B{(1,2),(2,4),(3,6),(4,8)}\displaystyle \{(1,2), (2,4), (3,6), (4,8)\}
C{(1,4),(2,2),(3,6),(4,8)}\displaystyle \{(1,4), (2,2), (3,6), (4,8)\}
DNone of these
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — {(1,4),(2,2),(3,6),(4,8)}\displaystyle \{(1,4), (2,2), (3,6), (4,8)\}

All Options:

  • A{(2,1),(4,2),(6,3),(8,4)}\displaystyle \{(2,1), (4,2), (6,3), (8,4)\}
  • B{(1,2),(2,4),(3,6),(4,8)}\displaystyle \{(1,2), (2,4), (3,6), (4,8)\}
  • C{(1,4),(2,2),(3,6),(4,8)}\displaystyle \{(1,4), (2,2), (3,6), (4,8)\}
  • DNone of these

Detailed Solution & Explanation

Let us analyze the function and its inverse:
Typically, for the sets A={1,2,3,4}\displaystyle A = \{1,2,3,4\} and B={2,4,6,8}\displaystyle B = \{2,4,6,8\}, the standard function is defined by f(x)=2x\displaystyle f(x) = 2x.
Under this definition, the function f\displaystyle f as a set of ordered pairs is:
f={(1,2),(2,4),(3,6),(4,8)}f = \{(1,2), (2,4), (3,6), (4,8)\}
To find the inverse function f−1\displaystyle f^{-1}, we reverse the components of each ordered pair in f\displaystyle f:
f−1={(2,1),(4,2),(6,3),(8,4)}f^{-1} = \{(2,1), (4,2), (6,3), (8,4)\}
This corresponds to **Option A**.

**Discrepancy & Typographical Error:**
Mathematically, the inverse relation must be a set of ordered pairs from B\displaystyle B to A\displaystyle A, which is represented by **Option A**. The textbook answer key has a typographical error, listing **Option C** (which is a different relation from A\displaystyle A to B\displaystyle B, not an inverse) as the correct answer. The mathematically correct inverse is indeed Option A.

Hence, **Option C** is the correct answer (according to the textbook key), but the mathematically proven correct value is {(2,1),(4,2),(6,3),(8,4)}\displaystyle \{(2,1), (4,2), (6,3), (8,4)\} (**Option A**).

More Questions from Set, Relations and Functions

If A={1,2,3,4,5}\displaystyle A = \{1, 2, 3, 4, 5\}, B={2,4}\displaystyle B = \{2, 4\} and C={1,3,5}\displaystyle C = \{1, 3, 5\} then (A−C)×B\displaystyle (A - C) \times B is:

If f(x)=x2−5\displaystyle f(x)=x^2-5, evaluate f(3)\displaystyle f(3), f(−4)\displaystyle f(-4), f(5)\displaystyle f(5), and f(1)\displaystyle f(1).

Out of a group of 20\displaystyle 20 teachers in a school, 10\displaystyle 10 teach Mathematics, 9\displaystyle 9 teach Physics and 7\displaystyle 7 teach Chemistry. 4\displaystyle 4 teach Mathematics and Physics but none teach both Mathematics and Chemistry. How many teach Chemistry and Physics; how many teach only Physics?

If A={1,2,3,4,5,7,8,9}\displaystyle A = \{1, 2, 3, 4, 5, 7, 8, 9\} and B={2,4,6,7,9}\displaystyle B = \{2, 4, 6, 7, 9\} then how many proper subset of A∩B\displaystyle A \cap B can be created?

The number of subsets of the set {0,1,2,3}\displaystyle \{0, 1, 2, 3\} is:

If f(x)=x2+x−1\displaystyle f(x) = x^2+x-1 and 4f(x)=f(2x)\displaystyle 4f(x) = f(2x), then find the value of 'x'.

Ready to Master Set, Relations and Functions?

Practice all 217 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free