+870 Let f be the reciprocal function:
\(\forall x \in \mathbb{R}^*, \\f(x)=\frac{1}{x}\)
I\ Calculate:
\(1) f(1) \\2) f(-\frac{1}{2}) \\3) f(10^{-6}) \\4) f(\sqrt{2}) \\5)f(\frac{\sqrt{5}}{5}) \)
Note: If you end up with roots or fractions, keep the fraction/radical, don't give the decimal form.
II\ Demonstrate that, for any strictly positive real number x, that \(\frac{1}{\sqrt{x}}=\frac{\sqrt{x}}{x}\)
1. 1/1 = 1
2. 1/(-1/2) = 1 x (-2/1) = -2
3. 1/(10^-6) = 1 x 10^6 = 1,000,000
4. 1/(sqrt2) = Sqrt(2)/2
5. 1/((sqrt5)/5) = 1 x 5/(sqrt5) = 5/sqrt5 = sqrt5
ii 1/sqrtx = 1/sqrtx x sqrtx/sqrtx = sqrtx/x
+870 Well done Guest, your answers are exact!
You deserved a 20/20 and a brownie:
