# Are these two functions the same,

• Oct 9th 2012, 12:45 PM
entrepreneurforum.co.uk
Are these two functions the same,
Can someone tell em if these two equations are the same

x = A[(s/δ)]^α/(1-α)

And

x = A[(δ/sA)^(1/(α-1))]^α

Thnaks

Edit: I can not seem to get TEX functions to work, sorry

• Oct 9th 2012, 06:18 PM
hollywood
Re: Are these two functions the same,
Without TEX, it's hard to figure out what your functions are. I'm guessing:

$\displaystyle x = A(\frac{s}{\delta})^\frac{\alpha}{1-\alpha}$

and

$\displaystyle x = A\left[(\frac{\delta}{sA})^{\frac{1}{\alpha-1}}\right]^\alpha$

To figure out if they're the same function, you use algebraic methods to put each in some standard form. The first one is:

$\displaystyle x = A(\frac{s}{\delta})^\frac{\alpha}{1-\alpha}= As^\frac{\alpha}{1-\alpha}\delta^\frac{-\alpha}{1-\alpha}$

The second one is:

$\displaystyle x = A\left[(\frac{\delta}{sA})^{\frac{1}{\alpha-1}}\right]^\alpha= A(\frac{\delta}{sA})^{\frac{\alpha}{\alpha-1}}= A\delta^{\frac{\alpha}{\alpha-1}}s^{\frac{-\alpha}{\alpha-1}}A^{\frac{-\alpha}{\alpha-1}}=A^{\frac{-1}{\alpha-1}}s^{\frac{-\alpha}{\alpha-1}}\delta^{\frac{\alpha}{\alpha-1}}$

So the answer is no, assuming I interpreted the functions correctly. If not, that's the general idea, so hopefully you can do it with the correct functions.

- Hollywood