Find the inverse function of $ f (x ) = x^2 - x - 2$, where x is equal to or larger than 1/2.
I tried to express it in form of $ (x - 1 )^2 = y + 2 $, but this is not true as the term in the middle is $ x $ and not $ 2x $.
Can anybody show me the full work solution?
Recall that $(x+a)^2 = x^2 +2ax +a^2$. Hence $x^2-x = x^2 -2 \cdot \frac{1}{2}x = \left( x - \frac{1}{2} \right)^2 -\frac{1}{4}$. Therefore $x^2-x-2=\left( x - \frac{1}{2} \right)^2 -\frac{1}{4} -2$. Can you conclude from here?