ok need some help i just cant seem to do these few questions, and i've left it until the last minute as it has to be in tomorrow! aargh! thanks for the help x

1) find the inverse and state the domain f(x) = 1 - 2^x , x E R

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- Nov 3rd 2009, 08:15 AMpop_91loads of help on functions needed
ok need some help i just cant seem to do these few questions, and i've left it until the last minute as it has to be in tomorrow! aargh! thanks for the help x

1) find the inverse and state the domain f(x) = 1 - 2^x , x E R - Nov 4th 2009, 12:31 AMGrandad
Hello pop_91Let $\displaystyle y = 1 - 2^x$

Then:$\displaystyle 2^x = 1-y$So the inverse function is:

$\displaystyle \Rightarrow x = \log_2(1-y)$

$\displaystyle f^{-1}(x) = \log_2(1-x)$I presume the question means the domain of the inverse function. The domain of $\displaystyle \log(z)$ is $\displaystyle z>0$, so here $\displaystyle 1-x>0$; i.e. the domain is $\displaystyle x<1, x \in \mathbb{R}$

Grandad - Nov 4th 2009, 07:59 AMpop_91
thanks so much :) x