# Math Help - loads of help on functions needed

1. ## loads 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

2. Hello pop_91
Originally Posted by pop_91
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
Let $y = 1 - 2^x$

Then:
$2^x = 1-y$

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