1. ### Find the inverse function of ##f(x) =x^4+2x^2##

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...
2. ### Invertible function

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...
3. ### Hi, I have a quick question about inverse functions.

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?
4. ### Inverse trigonometry question

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]...
5. ### How to find the inverse of a function

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
6. ### Finding inverse of a Sin function (problem from Mooculus)

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...
7. ### Checking for Accuracy in homework

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...