Inverted inverse

Algebra Level 2

If $f \left( \frac{x}{x+1} \right) = x^2-x$ , what is $f(0)+f(2)$ ?

1 solution

Arron Kau Staff
May 13, 2014

Let $\frac{x}{x+1} = 0$ , then $x=0$ . Thus, substituting $x=0$ into both sides of the given equation, we have

$f(0) = f \left( \frac{0}{0+1} \right) = 0^2-0 =0.$

Let $\frac{x}{x+1} = 2$ , then $x=2x+2 \;\;\; \Rightarrow x=-2$ . Thus, substituting $x=-2$ into both sides of the given equation, we have

$f(2) = f \left( \frac{-2}{-2+1} \right) = (-2)^2-(-2) =6.$

Therefore, $f(0)+f(2) = 6$ .

Is cross multiplication in the 3rd step allowed because we don't know the nature of x in the question ( whether or not it is non negative)?

toshali mohapatra - 4 years, 1 month ago