Question

If a function f satisfies $f\{f\left(x\right)\}=x+1$for all real values of $x$ and $f\left(0\right)=\frac{1}{2}$, then $f\left(1\right)$ is equal to

• A. $\frac{1}{2}$
• B. $1$
• C. $\frac{3}{2}$
• D. $2$
• E. $0$

Answer 1

The correct option is C

$\frac{3}{2}$

Explanation for correct option.

Given, $f\{f\left(x\right)\}=x+1$

Then put $x=\frac{1}{2}$

$$\begin{gathered} \Rightarrow f\left\{f\right(x\left)\right\}=x+1 \\ \Rightarrow f\left\{f\right(\frac{1}{2}\left)\right\}=\frac{1}{2}+1 \\ \Rightarrow f\left\{f\right(\frac{1}{2}\left)\right\}=\frac{3}{2} \end{gathered}$$

Hence the correct option is $\left(C\right)$