Question

The value of $\alpha (\ne 0)$ for which the function $f\left(x\right)=1+\alpha x$ is the inverse of itself is

• A. $-2$
• B. $2$
• C. $-1$
• D. $1$

Answer 1

The correct option is C $-1$

We have, $f\left(x\right)=1+\alpha x$

or, $y=1+\alpha x$

or, $x=\frac{y-1}{\alpha }$

Change $x$ with $y$ and $y$ with $x$

or, $y=\frac{x-1}{\alpha }$

or, $f^{-1}\left(x\right)=\frac{x-1}{\alpha }$

For, $f\left(x\right)=f^{-1}\left(x\right)$ value of $\alpha$ should be $-1.$

Hence, C is the correct option.