What is the inverse of f(x)=((arcsin(5x))^2)/4 ?

The inverse of f(x)=((arcsin(5x))^2)/4 is (sin(2sqrt(x)))/5 ,(sin(-2sqrt(x)))/5

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inverse of f(x)=((arcsin(5x))^2)/4

inverse

f (x) = \frac{( arcsin ( 5 x ) ) ^{2}}{4}

\frac{sin ( 2 x )}{5}, \frac{sin ( - 2 x )}{5}

Solution steps

Solve for

arcsin (5 x), y = \frac{arcsin ^{2} ( 5 x )}{4}

arcsin (5 x) = 2 y, arcsin (5 x) = - 2 y

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

5 x = sin (2 y), 5 x = sin (- 2 y)

Solve for

x, 5 x = sin (2 y)

Solve for

x, 5 x = sin (- 2 y)

\frac{sin ( 2 y )}{5}, \frac{sin ( - 2 y )}{5}

Substitute

y = x

\frac{sin ( 2 x )}{5}, \frac{sin ( - 2 x )}{5}

f (x) = \frac{2}{x - 5}

f (x) = \frac{x - 8}{x - 3}

f (x) = \frac{3 x - 5}{2 x}

- \frac{1}{3}

What is the inverse of f(x)=((arcsin(5x))^2)/4 ?
The inverse of f(x)=((arcsin(5x))^2)/4 is (sin(2sqrt(x)))/5 ,(sin(-2sqrt(x)))/5