CUET · MATHS · PYQ PAPER 2023

The inverse of the function \(f: R \rightarrow R\) given by \(f(x)=2 x+7\) is :

A \(2(x+7)\)
B \(\frac{x+7}{2}\)
C \(x-7\)
D \(\frac{x-7}{2}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{x-7}{2}\)

Step-by-step Solution

Detailed explanation

Let \(y = 2x+7\) Swap variables: \(x = 2y+7\) \(2y = x-7\) \(y = \frac{x-7}{2}\) \(f^{-1}(x) = \frac{x-7}{2}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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From CUET

Match List - I with List - II.

List - I	List - II
A. Simple and face centred cubic	I. \(\text{a} = \text{b} = \text{c}\)
B. Cubic and rhombohedral	II. \(\alpha = \beta = \gamma = 90°\)
C. Cubic and tetragonal	III. have only two crystallographic angle of \(90°\)
D. Hexagonal and monoclinic	IV. belong to the same crystalline system

Choose the correct answer from the options given below :

CUET 2023 Hard

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