Question

If $f\left(x\right)=2x$ and $f\left(f\right(x\left)\right)=x+1$, then the value of $x$ is

• A. $\frac{1}{3}$
• B. $1$
• C. $2$
• D. $3$
• E. $5$

Answer 1

The correct option is A $\frac{1}{3}$

Given $f\left(x\right)=2x$ and $f\left(f\right(x\left)\right)=x+1$

Then $f\left(f\right(x\left)\right)=x+1$

$\Rightarrow 2\left[f\right(x\left)\right]=x+1$

$\Rightarrow 2\left(2x\right)=x+1$

$\Rightarrow 4x=x+1$

$\Rightarrow x=\frac{1}{3}$