CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
If f(x) = 2x − 3, what is the inverse function f⁻¹(x)?
The inverse of f(x) = 2x − 3 is f⁻¹(x) = (x + 3)/2. Solving y = 2x − 3 for x gives x = (y + 3)/2, and substituting it back into f returns x, confirming the inverse.
- A(x − 3)/2
- B(x + 3)/2Correct
- C2x + 3
- D1/(2x − 3)
Explanation
Let y = 2x − 3. Then x = (y + 3)/2, so f⁻¹(x) = (x + 3)/2. Check: f((x+3)/2) = (x + 3) − 3 = x. Option A has the wrong sign for the constant, and option D is the reciprocal, not the inverse.
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