What is the inverse of f(x)=((arcsin(2x))^2)/2 ?

The inverse of f(x)=((arcsin(2x))^2)/2 is (sin(sqrt(2)sqrt(x)))/2 ,(sin(-sqrt(2)sqrt(x)))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

inverse of f(x)=((arcsin(2x))^2)/2

inverse

f (x) = \frac{( arcsin ( 2 x ) ) ^{2}}{2}

\frac{sin ( 2 x )}{2}, \frac{sin ( - 2 x )}{2}

Solution steps

Solve for

arcsin (2 x), y = \frac{arcsin ^{2} ( 2 x )}{2}

arcsin (2 x) = 2 y, arcsin (2 x) = - 2 y

arcsin (a) = b \Rightarrow a = sin (b)

2 x = sin (2 y), 2 x = sin (- 2 y)

Solve for

x, 2 x = sin (2 y)

Solve for

x, 2 x = sin (- 2 y)

\frac{sin ( 2 y )}{2}, \frac{sin ( - 2 y )}{2}

Substitute

y = x

\frac{sin ( 2 x )}{2}, \frac{sin ( - 2 x )}{2}

What is the inverse of f(x)=((arcsin(2x))^2)/2 ?
The inverse of f(x)=((arcsin(2x))^2)/2 is (sin(sqrt(2)sqrt(x)))/2 ,(sin(-sqrt(2)sqrt(x)))/2