The inverse function f^{-1} of f(x) = 3y is:

Option b: y/3. Solution: The function is given as y = f(x) = 3x. To find the inverse function f^{-1} in terms of y, we solve for x in terms of y: y = 3x implies x = y/3 Therefore, the inverse function is: f^{-1}(y) = y/3 This corresponds to Option B. Hence, Option B is the correct answer.

The inverse function $f^{-1}$ of $f(x) = 3y$ is:

The correct answer is Option b: $y/3$. The function is given as $y = f(x) = 3x$. To find the inverse function $f^{-1}$ in terms of $y$, we solve for $x$ in terms of $y$: $$y = 3x \implies x = \frac{y}{3}$$ Therefore, the inverse function is: $$f^{-1}(y) = \frac{y}{3}$$ This corresponds to Option B. Hence, **Option B** is the correct answer.

Set, Relations and FunctionsPYQ Nov. 20Question 1964 of 217

All Questions

The inverse function $\displaystyle f^{-1}$ of $\displaystyle f(x) = 3y$ is:

Options

\displaystyle 1/3y

\displaystyle y/3

\displaystyle -3y

\displaystyle 1/y

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Correct Answer

✅ Option b — $\displaystyle y/3$

All Options:

A $\displaystyle 1/3y$
B $\displaystyle y/3$
C $\displaystyle -3y$
D $\displaystyle 1/y$

Detailed Solution & Explanation

The function is given as

\displaystyle y = f(x) = 3x

.
To find the inverse function

\displaystyle f^{-1}

in terms of

\displaystyle y

, we solve for

\displaystyle x

in terms of

\displaystyle y

y = 3x \implies x = \frac{y}{3}

Therefore, the inverse function is:

f^{-1}(y) = \frac{y}{3}

This corresponds to Option B.
Hence, **Option B** is the correct answer.

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The inverse function f−1\displaystyle f^{-1}f−1 of f(x)=3y\displaystyle f(x) = 3yf(x)=3y is: