AoPS Wiki talk:Problem of the Day/June 9, 2011
Problem
AoPSWiki:Problem of the Day/June 9, 2011
Solution
Let . Therefore, . Now, let be the inverse function of , so that . However, the in the LHS cancels out by the definition of an inverse function. Therefore, we have . Now we must find . Again by the definition of an inverse function, we have , and , so . Solving, we find that . Plugging this in to yields .
Another solution:
We know that f(x) is of the form ax+b, so we can start by plugging in x=1 which yields f(1)=7 and plugging in x=-1 gives f(0)=3, using the slope formula we can get f(x)=4x+3