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})

f (x) = \frac{9 x - 1}{x + 6}

f (x) = \frac{x}{9 x - 7}

\frac{5 - s}{( s + 3 ) ( s - 1 )}

\frac{x ^{3}}{x ^{3} + 5}

y^{- 1} = e^{\frac{x + 4}{3}} - 2

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))