# determining the domain of inverse function of x

• Oct 31st 2012, 10:18 AM
kingsolomonsgrave
determining the domain of inverse function of x
\$\displaystyle f(x)=1+sqrt(2+3*x)\$ for x> or equal to -2/3

I said the domain is R which is wrong.

however I got the inverse to be \$\displaystyle y=((x-1)^2)/3\$ which seems to be defined everywhere

Do you keep the restriction on the domain of the original function for the inverse?

thanks!
• Oct 31st 2012, 11:16 AM
emakarov
Re: determining the domain of inverse function of x
First, the inverse function is y = ((x - 1)^2 - 2) / 3. Second, how can the domain of the inverse function be all reals if the original function returns only values >= 1? Formally, when you are solving the equation to find the inverse function, note that x - 1 = sqrt(2 + 3x) is not equivalent to (x - 1)^2 = 2 + 3x. More precisely, every pair (x, y) that satisfies the first equation also satisfies the second one but not vice versa. This is why you end up with an equation that has more solutions (x, y) than the original one.