Homework Statement
Find the inverse function of ##f(x) =x^4+2x^2, x>0##
Homework Equations
##f(f^{-1}(x)) = x##
The Attempt at a Solution
My only progress so far is
##x^4+2x^2 = x^2(x^2+2)##
Then I am stuck.
Since my progress is close to nothing so I don’t expect a complete...
Homework Statement
Find the smallest value of b so that the function f(x) = x^3 + 9x^2 + bx + 8 is invertible.
Homework Equations
The Attempt at a Solution
I know that the function has to be only increasing/decreasing, and I think it is needed to find the derivative of the function. I do...
One of our homework problem asks:
If f is a one-to-one function such that f(-3)=5 , find x given that f^-1 (5)=3x-1.
Here's how I attempted to solve the problem:
-3=3x-1
3x=-2
x=-2/3
Is this the correct way to solve the problem?
Homework Statement
If 1/2<=x<=1
, then cos-1[ x/2 + (√(3-3x2))/2] + cos-1 x is equal to?
Homework Equations
The Attempt at a Solution
Substituting x=cosθ
= cos-1(cosθ) + cos-1 [ cos(θ)/2 + (√(3(1-cos2(θ)))/2]
= θ + cos-1 [cos (π/3) cos θ + sin (π/3) sinθ]...
T(t) = Ts+(98.6 – Ts)e-kt
rewrite in the form t=g-1(T)
In trying to understand how to find the inverse of this but am having a hard time, please advise.
Thanks,
Kupkake303
I'm working through the problems in the Mooculus textbook as revision for Calculus I & there seems to be something wrong with how I'm manipulating the function to find its inverse in the following example.
Homework Statement
The height in meters of a person off the ground as they ride a Ferris...
I noticed the scan was cut off on the second image at the bottom right, but I came up with x= 31/5
My first test in Calc I begins tomorrow and I want to know that I'm headed in the right direction. I think I understand to some extent how logarithms can be expanded and condensed though I'm...