$y=a\mathrm{cos}(x)+b\mathrm{sin}(2x)$

to give $x=f(y)$?

Chaim Ferguson
2022-10-25
Answered

Can anyone invert

$y=a\mathrm{cos}(x)+b\mathrm{sin}(2x)$

to give $x=f(y)$?

$y=a\mathrm{cos}(x)+b\mathrm{sin}(2x)$

to give $x=f(y)$?

You can still ask an expert for help

Amaya Vance

Answered 2022-10-26
Author has **6** answers

Notice that the inverse trigonometric functions are not actually the inverse of trigonometric functions. For example, sinx doesn't actually have an inverse as it fails the horizontal line test. The inverse only exists when we restrict sinx's domain to be $[-{\displaystyle \frac{\pi}{2}},{\displaystyle \frac{\pi}{2}}]$

In your function $f(x)=a\mathrm{cos}x+b\mathrm{sin}2x$, the domain is $\mathbb{R}$, and it's a periodic function, so it clearly does not have an inverse function. The same goes with $g(x)=a\mathrm{sin}x+b\mathrm{sin}2x$

In your function $f(x)=a\mathrm{cos}x+b\mathrm{sin}2x$, the domain is $\mathbb{R}$, and it's a periodic function, so it clearly does not have an inverse function. The same goes with $g(x)=a\mathrm{sin}x+b\mathrm{sin}2x$

asked 2021-09-07

Whether each of these functions is a bijection from R to R.

a) $f(x)=-3x+4$

b) $f\left(x\right)=-3{x}^{2}+7$

c) $f(x)=\frac{x+1}{x+2}$

$d)f\left(x\right)={x}^{5}+1$

asked 2021-09-10

A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at 10, the average attendance had been 27,000. When ticket prices were lowered to10,the average attend ance had been 27,000.When ticket prices were lowered to 8, the average attendance rose to 33,000. How should ticket prices be set to maximize revenue?

asked 2021-06-11

Find the linear approximation of the function

asked 2021-09-08

Explain why the function is differentiable at the given point. Then find the linearization L(x, y) of the function at
that point.
$f(x,y)=1+xIn(xy-5),(2,3)$

asked 2021-08-13

Find all of the points on the x-axis which are 4 units from the point (-1, 1).

asked 2021-09-22

What is the minimum vertical distance between the parabolas $y={x}^{2}+1$ and $y=x-{x}^{2}$

asked 2021-09-08

Classify each following function:

a)

b)

c)

d)

e)

f)