Question

If $f: R \to R$ is defined by $f(x) = 3x - 4$, then $f^{-1(x)$ is:

• A. $\frac{x+4}{3}$
• B. $\frac{x-4}{3}$
• C. $3x+4$
• D. None of these

Hint:

The inverse function undoes the operations of the original function in reverse order.

Answer 1

The Correct Option is A

Step 1: Concept
To find the inverse, set $y = f(x)$ and solve for $x$ in terms of $y$.
Step 2: Analysis
$y = 3x - 4 \Rightarrow y + 4 = 3x \Rightarrow x = \frac{y+4}{3}$.
Step 3: Conclusion
Replacing $y$ with $x$, we get $f^{-1}(x) = \frac{x+4}{3}$.
Final Answer: (A)