Understand Derivative of Inverse Trig Functions with Our Experts!

Compute the inverse function of the following polynomial on $[0, 1]$ ?
$f (x) = α x^{3} - 2 α x^{2} + (α + 1) x$
(where $α$ is within $] 0, 3 [$ )

Jayla Christensen 2022-06-22

$\frac{1}{x}$ and its inverse breaking a rule of inverse functions?

Davon Irwin 2022-06-18

Let $(X, ϕ)$ and $(Y, σ)$ be metric spaces, and let
$f, f_{1}, f_{2}, \dots$ bijective function with inverse functions $g, g_{1}, g_{2}, \dots$
$f_{n} \to f$ pointwise for $n \to \infty$ .
And all involved functions are continuous. Does it hold that $g_{n} \to g$ pointwise for $n \to \infty$ ?

Izabella Ponce 2022-06-16

Why doesn't inverse $t a n$ of $t a n (124) = - 56$ degrees instead of $124$ degrees? Doesn't the inverse function cancel the tan function?

Gybrisysmemiau7 2022-06-15

There are two functions $f : Q \to Q ∖ {- 1}$ and $g : Q \to Q ∖ {1}$ .
$g (x) = \frac{f (x)}{f (x) + 1} .$
Prove that if there is a inverse function for $f$ , then g is also inverse.

landdenaw 2022-06-13

There are functions for which it is possible for only one of these to be true.
give an example of such a function

mllewestblam2 2022-06-04

$g (x) = \frac{1}{x - 2} + 5 (x > 2)$
Find the inverse function $g^{- 1}$ specifying the rule domain and image set.

Estrella Le 2022-06-04

Is it true that for $F : R^{n} \to R^{m}$ which has an inverse function $F^{- 1} : R^{m} \to R^{n}$ , says $F$ is diﬀerentiable at $a \in R^{n}$ and $F^{- 1}$ is diﬀerentiable at $b = F (a) \in R^{m}$ ，then $m$ must be equal to $n$ ?

Alani Patrick 2022-06-04

Let $f : R \to R$ is a strictly increasing function and $f^{- 1}$ is its inverse function. It satisfies:
$f (x_{1}) + x_{1} = a$ ; $f^{- 1} (x_{2}) + x_{2} = a$
What is the value of $x_{1} + x_{2}$ ?

Giancarlo Todd 2022-06-01

Finding the inverse function to $f (x) = x^{2} - 6 x$

Jordyn Calhoun 2022-05-31

Let $f (x) = x^{3} + x$ . If h is the inverse function of $f$ , then $h^{'} (2) =$ =?
The derivative of $f$ is: $3 x^{2} + 1$ . But, how do I find the $f^{- 1} x$ ?

reryfaikear 2022-05-27

${\begin{cases} u = e^{x} c o s (y) \\ v = e^{x} s i n (y) \end{cases}$
Determine the inverse functions, and compute the Jacobian of the inverse functions of these functions.

Reese Estes 2022-05-09

Find the derivative to the inverse function in $(π / 4) - 1$ .

Annabel Sullivan 2022-05-09

Let $f (x) = \frac{1}{4} x^{3} + 12 x + 6$ and let $y = f^{- 1} (x)$ be the inverse function of $f$ . Determine the $x$ -coordinates of the two points on the graph of the inverse function where the tangent line is perpendicular to the straight line $y = - 24 x - 32$ .

kulisamilhh 2022-05-03

How can be helpful inverse functions determination by integral?
$f^{- 1} (x) = \int \frac{1}{f^{'} (f^{- 1} (x))} d x + c .$

coraletsmmh 2022-04-30

Let $f (x)$ be a differential and an invertible function, such that $f^{″} (x) > 0$ and $f^{'} (x) > 0$ .
Prove
$f^{- 1} (\frac{x_{1} + x_{2} + x_{3}}{3}) > \frac{f^{- 1} (x_{1}) + f^{- 1} (x_{2}) + f^{- 1} (x_{3})}{3}$

indimiamimactjcf 2022-04-07

Im trying to find $2$ functions $f, g$ such that $f$ and $g$ both not linear, and $f, g : R \to R$ and onto, such that $f (g (x)) = x, g (f (x)) = x$
( $f$ is the inverse function of $g$ ).
There exists such functions?

Reese Estes 2022-04-07

the notation $(f + g)^{- 1}$ for the inverse function

When you are feeling lost solving inverse functions for your differential calculus class, the only way to see some rationale is to look through the questions and answers by taking a detailed approach. If it does not make much sense, you should use equations and graphs as you are proving inverse functions. It will help you to see where things get challenging as you can compare the questions to the answers provided. Just remember that the purpose here is to "undo" another function, which makes the function inverse. Once you learn to reverse-engineer, your general calculus challenges will get easier!

Differential Calculus

Solving Inverse Functions with Examples and Solutions