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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

inverse

\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}

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