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

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

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

inverse

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

sin (x), - sin (x)

Solution steps

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

x^{2} = sin (y)

Solve for

x, x^{2} = sin (y)

sin (y), - sin (y)

Substitute

y = x

sin (x), - sin (x)

y = x^{2} + 12 x

f (x) = 6 (x - 1)

x + 4 - 10

f (x) = 36 \cdot 1 3^{x}

9 x^{2} + 5 x + 2

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