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 $\displaystyle y = 1 - 2^x$
Then: $\displaystyle 2^x = 1-y$
$\displaystyle \Rightarrow x = \log_2(1-y)$
So the inverse function is:$\displaystyle f^{-1}(x) = \log_2(1-x)$
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