Question:
If $f:\mathbb{R}\rightarrow\mathbb{R}$ is given by $f(x)=7x+8$ and $f^{-1}(12)=\dfrac{k}{7}$, then the value of $k$ is
If $f:\mathbb{R}\rightarrow\mathbb{R}$ is given by $f(x)=7x+8$ and $f^{-1}(12)=\dfrac{k}{7}$, then the value of $k$ is
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For linear functions, inverse functions are obtained by simple rearrangement.
Updated On: Mar 28, 2026
- $7$
- $1$
- $4$
- $8$
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The Correct Option is C
Solution and Explanation
Step 1: Finding the inverse function.
\[ y = 7x + 8 \] Interchanging $x$ and $y$: \[ x = 7y + 8 \Rightarrow y = \frac{x-8}{7} \]
Step 2: Evaluating $f^{-1(12)$.}
\[ f^{-1}(12) = \frac{12-8}{7} = \frac{4}{7} \]
Step 3: Comparing with given value.
\[ \frac{k}{7} = \frac{4}{7} \Rightarrow k = 4 \]
Step 4: Conclusion.
The value of $k$ is $4$.
\[ y = 7x + 8 \] Interchanging $x$ and $y$: \[ x = 7y + 8 \Rightarrow y = \frac{x-8}{7} \]
Step 2: Evaluating $f^{-1(12)$.}
\[ f^{-1}(12) = \frac{12-8}{7} = \frac{4}{7} \]
Step 3: Comparing with given value.
\[ \frac{k}{7} = \frac{4}{7} \Rightarrow k = 4 \]
Step 4: Conclusion.
The value of $k$ is $4$.
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