2. ### A Integral with an inverse function limit

Hello, I have tried the integral below with Mathematica and it gives me the following solution: ##\frac{d}{dc}\int_{z^{-1}(c)}^{1} z(x)dx = -\frac{c}{z'(z^{-1}(c))}## I am not quite sure where it gets it from...I think it can be separated and with differentiation the first part will be zero...
3. ### F bijective <=> f has an inverse

Homework Statement Proof that: f has an inverse ##\iff## f is a bijection Homework Equations /definitions[/B] A) ##f: X \rightarrow Y## If there is a function ##g: Y \rightarrow X## for which ##f \circ g = f(g(x)) = i_Y## and ##g \circ f = g(f(x)) = i_X##, then ##g## is the inverse...
4. ### Inverse trig Inequality

Homework Statement Solution set of the inequality (cot-1(x))2 -(5 cot-1(x)) +6 >0 is? Homework Equations The Attempt at a Solution Subs cot-1(x)=y We get a quadratic inequality in y. y2-5y+6>0 (y-2)(y-3)>0 Using the wavy curve method, the solution set is...
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. ### 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...