Question

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

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

Answer 1

Answer: (C)

Given, $f\{f(x)\}=x+1$ ...(i)
$\therefore$ $f(f(0))=0+1$
$\Rightarrow$ $f\left(\frac{1}{2}\right)=1$
$\left[\because f(0)=\frac{1}{2}\right]$
Now, put $x=\frac{1}{2}$ in Eq. (i), we get
$f\left\{f\left(\frac{1}{2}\right)\right\}=\frac{1}{2}+1$
$\Rightarrow$ $f(1)=\frac{3}{2}$