If f(x): N to R is a function defined as f(x) = 4x+3, forall x in N, then f^{-1}(x) is:

Option c: x-3/4. Solution: To find the inverse function f^{-1}(x), we set the function equal to y: y = 4x + 3 Now we solve for x in terms of y: y - 3 = 4x x = y-3/4 Replacing the variable y with x to express the inverse function in terms of x, we get: f^{-1}(x) = x-3/4 Hence, Option C is the correct answer.

If $f(x): N \to R$ is a function defined as $f(x) = 4x+3$, $\forall x \in N$, then $f^{-1}(x)$ is:

The correct answer is Option c: $\frac{x-3}{4}$. To find the inverse function $f^{-1}(x)$, we set the function equal to $y$: $$y = 4x + 3$$ Now we solve for $x$ in terms of $y$: $$y - 3 = 4x$$ $$x = \frac{y-3}{4}$$ Replacing the variable $y$ with $x$ to express the inverse function in terms of $x$, we get: $$f^{-1}(x) = \frac{x-3}{4}$$ Hence, **Option C** is the correct answer.

Set, Relations and FunctionsPYQ Jun 23Question 1972 of 217

All Questions

If $\displaystyle f(x): N \to R$ is a function defined as $\displaystyle f(x) = 4x+3$ , $\displaystyle \forall x \in N$ , then $\displaystyle f^{-1}(x)$ is:

Options

\displaystyle \frac{4+x}{4}

\displaystyle \frac{x+3}{4}

\displaystyle \frac{x-3}{4}

\displaystyle \frac{x+4}{4}

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — $\displaystyle \frac{x-3}{4}$

All Options:

A $\displaystyle \frac{4+x}{4}$
B $\displaystyle \frac{x+3}{4}$
C $\displaystyle \frac{x-3}{4}$
D $\displaystyle \frac{x+4}{4}$

Detailed Solution & Explanation

To find the inverse function

\displaystyle f^{-1}(x)

, we set the function equal to

\displaystyle y

y = 4x + 3

Now we solve for

\displaystyle x

in terms of

\displaystyle y

y - 3 = 4x

x = \frac{y-3}{4}

Replacing the variable

\displaystyle y

with

\displaystyle x

to express the inverse function in terms of

\displaystyle x

, we get:

f^{-1}(x) = \frac{x-3}{4}

Hence, **Option C** is the correct answer.

Ready to Master Set, Relations and Functions?

Practice all 217 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free

If f(x):N→R\displaystyle f(x): N \to Rf(x):N→R is a function defined as f(x)=4x+3\displaystyle f(x) = 4x+3f(x)=4x+3, ∀x∈N\displaystyle \forall x \in N∀x∈N, then f−1(x)\displaystyle f^{-1}(x)f−1(x) is: