Set, Relations and FunctionsMTP Nov 21Question 1980 of 217
All Questions

If f(x)=x2−1\displaystyle f(x) = x^2-1 and g(x)=2x+3\displaystyle g(x) = 2x+3 then gof(3)\displaystyle gof(3)

Options

A71
B61
C41
D19
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — 61

All Options:

  • A71
  • B61
  • C41
  • D19

Detailed Solution & Explanation

Let us analyze the literal printed question and the likely intended full question:

**1. Literal Evaluation of g(f(3))\displaystyle g(f(3)):**
Given the functions:
f(x)=x2−1f(x) = x^2 - 1
g(x)=2x+3g(x) = 2x + 3
We evaluate f(3)\displaystyle f(3):
f(3)=32−1=9−1=8f(3) = 3^2 - 1 = 9 - 1 = 8
Now we substitute this into g(x)\displaystyle g(x) to find g(f(3))\displaystyle g(f(3)):
g(f(3))=g(8)=2(8)+3=16+3=19g(f(3)) = g(8) = 2(8) + 3 = 16 + 3 = 19
This corresponds to **Option D**.

**2. Source of Discrepancy & Truncation Error:**
This question (from MTP Nov 21) is a truncated version of a well-known past exam question (e.g., PYQ Dec 21, which is Question 2 in this set). The full question was:
Find [f∘g](3)−[g∘f](−3)\text{Find } [f \circ g](3) - [g \circ f](-3)
Let's solve the full question:
- g(3)=2(3)+3=9  ⟹  f(g(3))=92−1=80\displaystyle g(3) = 2(3) + 3 = 9 \implies f(g(3)) = 9^2 - 1 = 80
- f(−3)=(−3)2−1=8  ⟹  g(f(−3))=2(8)+3=19\displaystyle f(-3) = (-3)^2 - 1 = 8 \implies g(f(-3)) = 2(8) + 3 = 19
- Difference: 80−19=61\displaystyle 80 - 19 = 61.
This matches **Option B** (61).

Because the question was truncated during printing, the literal answer is 19\displaystyle 19 (Option D), but the official exam key retains the original value **Option B** (61) based on the untruncated problem.

Hence, **Option B** is the correct answer (according to the textbook key), but the mathematically proven correct value for the printed text is 19\displaystyle 19 (**Option D**).

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