# If f(x/(x+1))=(x-1)^2, what is f(3)?

Jun 4, 2018

$\frac{25}{4} = 6.25$.

#### Explanation:

Given that, $f \left(\frac{x}{x + 1}\right) = {\left(x - 1\right)}^{2}$.

We require the value of $f \left(3\right)$.

Clearly the corresponding $x$ for this can be obtained by solving

$\frac{x}{x + 1} = 3$.

$\therefore x = 3 x + 3$.

$\therefore - 2 x = 3 , \text{ giving, } x = - \frac{3}{2}$.

Subst.ing $x = - \frac{3}{2}$ in the formula for $f$, we get,

$f \left(\frac{- \frac{3}{2}}{- \frac{3}{2} + 1}\right) = f \left(- \frac{3}{2} \div - \frac{1}{2}\right) = f \left(3\right) = {\left(- \frac{3}{2} - 1\right)}^{2}$.

$\Rightarrow f \left(3\right) = \frac{25}{4} = 6.25$.

Enjoy Maths.!

Jun 4, 2018

$f \left(3\right) = \frac{25}{4}$

#### Explanation:

We are looking for what value of $x$ gives

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

Solve the equation:

$x = 3 x + 3$

$- 2 x = 3$

$x = - \frac{3}{2}$

Now simply plug $x = - \frac{3}{2}$ into the formula

$f \left(3\right) = {\left(- \frac{3}{2} - 1\right)}^{2} = \frac{25}{4}$