Question

If a function $f:\mathbb{R} \to \mathbb{R}$ is defined by $f(x) = \dfrac{4x}{5} + 3$, then $f^{-1}(x) =$

• A. $\dfrac{5(x+3)}{4}$
• B. $\dfrac{5(x-3)}{4}$
• C. $\dfrac{4(x+3)}{5}$
• D. $\dfrac{4(x-3)}{5}$

Hint:

To find the inverse of a function, interchange $x$ and $y$ and solve for $y$.

Answer 1

The Correct Option is B

Step 1: Writing the given function.
\[ y = \frac{4x}{5} + 3 \]
Step 2: Interchanging $x$ and $y$.
\[ x = \frac{4y}{5} + 3 \]
Step 3: Solving for $y$.
\[ x - 3 = \frac{4y}{5} \Rightarrow y = \frac{5(x-3)}{4} \]
Step 4: Conclusion.
\[ f^{-1}(x) = \frac{5(x-3)}{4} \]