ok i have a function f(x)= x^4+x^3+1 that i need to find the inverse of, only thing is that when i switch the x and the y to solve, it gets real messy. any help would be appreciated. thanks
Well it depends on the domain you choose.The function as it is, is a MANY-ONE and INTO function and therefore you cannot find its inverse.You need to choose a suitable domain and corresponding codomain so that the function could be ONE-ONE and ONTO.
Even then you end up only proving existence of inverse and may not be able to get the actual inverse.
a) show that f is one to one
b) let g(x) = the inverse of f(x) and define F(x) = f(2g(x)). find an equation for the tangent line to y = F(x) at x = 3.
so to find the equation of a line i just need the point and the slope. first in getting the slope i use the chain rule to give me F'(x) = f'(2g(x)) * 2g'(x) * g'(x)? i think well i hope i executed the chain rule properly, its been a while since ive used it. but i think once i find the slope then i would plug in 3 to get the y-value and then substitute into the point slope formula?