Just need help to start this problem.
Given f(x)=x^3+3x+1 is one to one. Without actually determining the inverse function f^-1, compute the following (show and discuss your work.
f^-1(-3)
solve:
x^3 + 3x + 1 = -3
x^3 + 3x + 4 = 0
let x = 1 ---> 1+3+4 = 0 ? no
let x = -1 ---> -1-3+4 = 0 , yeahh
x^3 + 3x + 4 = (x+1)(x^2 - x + 4) = 0
so x=-1 or x is a complex number
so f^-1 (-3) = -1
check:
f(x) = y = x^3 + 3x + 1
f(-1) = -1 -3 + 1 = -3
the inverse is:
x = y^3 + 3y + 1
plug in x = -3
I solved this above to get -1