Functions

Easymathematics

If f: R → R is defined by f(x) = 3x - 5, then f⁻¹(x) equals

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(x + 5)/3

(x - 5)/3

3x + 5

(5 - x)/3

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About This Question

Subject: mathematics
Chapter: sets, relations and functions
Topic: functions
Difficulty: Easy
Year: 2025

Solution

Correct Answer:

(x + 5)/3

Identify Inverse Method: To find the inverse of $y = f (x)$ , solve the equation for $x$ in terms of $y$ .
Set up Equation: $y = 3 x - 5$ .
Algebraic Manipulation:
- Add 5 to both sides: $y + 5 = 3 x$
- Divide by 3: $x = \frac{y + 5}{3}$ .
Final Step: Swap variables to express in $x$ : $f^{- 1} (x) = \frac{x + 5}{3}$ .

Verification: $f (f^{- 1} (x)) = 3 (\frac{x + 5}{3}) - 5 = x + 5 - 5 = x$ .

This easy difficulty mathematics question is from the chapter sets, relations and functions, covering the topic of functions. It appeared in the 2025 exam.

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