What is the inverse of 3sin(x^2)-2 ?

The inverse of 3sin(x^2)-2 is sqrt(arcsin((x+2)/3)),-sqrt(arcsin((x+2)/3))

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inverse of 3sin(x^2)-2

inverse

3 sin (x^{2}) - 2

arcsin (\frac{x + 2}{3}), - arcsin (\frac{x + 2}{3})

Solution steps

Solve for

sin (x^{2}), y = 3 sin (x^{2}) - 2

sin (x^{2}) = \frac{y + 2}{3}

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

x^{2} = arcsin (\frac{y + 2}{3})

Solve for

x, x^{2} = arcsin (\frac{y + 2}{3})

arcsin (\frac{y + 2}{3}), - arcsin (\frac{y + 2}{3})

Substitute

y = x

arcsin (\frac{x + 2}{3}), - arcsin (\frac{x + 2}{3})

What is the inverse of 3sin(x^2)-2 ?
The inverse of 3sin(x^2)-2 is sqrt(arcsin((x+2)/3)),-sqrt(arcsin((x+2)/3))