Hello! I am having troubles with a question I just got in my AP calc class. It is:
Let f(x) = x5 + 2x3 + x + 1
a) find f -1(3) and (f -1)'(3)
The Attempt at a Solution
Okay so my first idea was obviously to switch the x and y in f(x) giving me x = y5 + 2y3 + y + 1 however, it is clearly too difficult to isolate y in this equation.
So i was thinking, for f -1(3) , if I substitute 3 for y in the original equation, giving me 3 = x5 + 2x3 + x + 1 and solve for the zeroes, will that give me my answer to f -1(3) ? And then for (f -1)'(3), i would set the derivative of f(x) to 3, and solve for the zeroes, which would look like 3 = 5x4 + 6x2 + 1
Would doing these things with f(x) effectively give me the answers to these two inverse problems?
Any help would be appreciated :)