If f(p)=1/1-p, then f^{-1} is

Option b: (p-1)/p. Solution: To find the inverse function f^{-1}, we set x = f(p) and solve for p in terms of x: x = 1/1 - p Take the reciprocal of both sides: 1/x = 1 - p Add p to both sides and subtract 1/x: p = 1 - 1/x Find a common denominator to simplify: p = x - 1/x To express the inverse function in terms of the variable p (as shown in the options): f^{-1}(p) = p - 1/p Hence, Option B is the correct answer.

If $f(p)=\frac{1}{1-p}$, then $f^{-1}$ is

The correct answer is Option b: $(p-1)/p$. To find the inverse function $f^{-1}$, we set $x = f(p)$ and solve for $p$ in terms of $x$: $$x = \frac{1}{1 - p}$$ Take the reciprocal of both sides: $$\frac{1}{x} = 1 - p$$ Add $p$ to both sides and subtract $\frac{1}{x}$: $$p = 1 - \frac{1}{x}$$ Find a common denominator to simplify: $$p = \frac{x - 1}{x}$$ To express the inverse function in terms of the variable $p$ (as shown in the options): $$f^{-1}(p) = \frac{p - 1}{p}$$ Hence, **Option B** is the correct answer.

Set, Relations and FunctionsMTP Dec 22 - Series IQuestion 1995 of 217

All Questions

If $\displaystyle f(p)=\frac{1}{1-p}$ , then $\displaystyle f^{-1}$ is

Options

\displaystyle 1-p

\displaystyle (p-1)/p

\displaystyle p/(p-1)

\displaystyle 1/p

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Correct Answer

✅ Option b — $\displaystyle (p-1)/p$

All Options:

A $\displaystyle 1-p$
B $\displaystyle (p-1)/p$
C $\displaystyle p/(p-1)$
D $\displaystyle 1/p$

Detailed Solution & Explanation

To find the inverse function

\displaystyle f^{-1}

, we set

\displaystyle x = f(p)

and solve for

\displaystyle p

in terms of

\displaystyle x

x = \frac{1}{1 - p}

Take the reciprocal of both sides:

\frac{1}{x} = 1 - p

Add

\displaystyle p

to both sides and subtract

\displaystyle \frac{1}{x}

p = 1 - \frac{1}{x}

Find a common denominator to simplify:

p = \frac{x - 1}{x}

To express the inverse function in terms of the variable

\displaystyle p

(as shown in the options):

f^{-1}(p) = \frac{p - 1}{p}

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

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