loads of help on functions needed

pop_91 · #1 $Old$ November 3rd, 2009, 09:15 AM

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

Grandad · #2 $Old$ November 4th, 2009, 01:31 AM

Hello pop_91

Quote:

Originally Posted by pop_91 $View Post$

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 $x<1, x \in \mathbb{R}$

Grandad

pop_91 · #3 $Old$ November 4th, 2009, 08:59 AM

thanks so much

x