CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
Let f(x) = 2x + 3. What is the inverse function f⁻¹(x)?
The inverse of f(x) = 2x + 3 is (x − 3)/2. Solving y = 2x + 3 for x gives x = (y − 3)/2, and renaming the variable gives the inverse function.
- A(x − 3)/2Correct
- B(x + 3)/2
- C2x − 3
- D1/(2x + 3)
Explanation
Put y = 2x + 3, so x = (y − 3)/2. Interchanging variables gives f⁻¹(x) = (x − 3)/2. Check: f(f⁻¹(4)) = f(0.5) = 4. Option D is the reciprocal, not the inverse.
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