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

The inverse of f(x)=3sin(3x-2) is (arcsin(x/3)+2)/3

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inverse of f(x)=3sin(3x-2)

inverse

f (x) = 3 sin (3 x - 2)

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

Solution steps

Solve for

sin (3 x - 2), y = 3 sin (3 x - 2)

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

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

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

Solve for

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

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

Substitute

y = x

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

f (x) = (1 - x)

f (x) = \frac{6 x + 7}{5 x - 6}

3 x + 4 y = 2

(x^{2} + 2 x - 1) (2 x^{2} - 3 x + 6)

(7, 3), (12, 15)

What is the inverse of f(x)=3sin(3x-2) ?
The inverse of f(x)=3sin(3x-2) is (arcsin(x/3)+2)/3