SOLUTION: Let F(x)= x^3-2x+1, and g(x)=x^5-x+3. Find F^-1(x) and g^-1(x). Please help me thank's

Algebra ->  Functions -> SOLUTION: Let F(x)= x^3-2x+1, and g(x)=x^5-x+3. Find F^-1(x) and g^-1(x). Please help me thank's      Log On


   

Question 30491: Let F(x)= x^3-2x+1, and g(x)=x^5-x+3. Find F^-1(x) and g^-1(x).
Please help me
thank's
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
I have plotted both curves for you. I have done this to show you that picking certain y-values gives you multiple values of x. This contravenes the one basic requirement of any function...it must NOT be one-to-many.

+graph%28300%2C300%2C-4%2C4%2C-4%2C4%2Cx%5E3-2x%2B1%29+

+graph%28300%2C300%2C-4%2C4%2C-4%2C10%2Cx%5E5-x%2B3%29+

Hence, strictly, neither of these functions have inverse functions. Now, you could get round that by narrowing the domain of the functions, such that the one-to-many region of the curves is not included, but forgeet that: just say:

There is no inverse because the function is ONE-TO-MANY. If your teacher argues, then pass them over to me here and i shall argue with them.

jon.