The scared function!

Algebra Level pending

If $f(x)=\dfrac{1}{1-x}$ , then find the value of $f(f(f(5)))$ .

-\dfrac{1}{4}

\dfrac{1}{5}

-\dfrac{4}{5}

1 solution

Skanda Prasad
Jul 2, 2017

Substitute $x$ as $\dfrac{1}{1-x}$ in $f(x)$ $2$ more times giving us the value finally as $x$ Therefore, $x=5$

$f(f(x))=\dfrac{x-1}{x}$ .

Substituting $\dfrac{1}{1-x}$ again, we get $f(f(f(x)))=\dfrac{\dfrac{1}{1-x}-1}{\dfrac{1}{1-x}}=x$ .

Hence, $f(f(f(5)))$ $=$ $5$ .