What is the inverse of f(x)=3sin(2x-1) ?

The inverse of f(x)=3sin(2x-1) is (arcsin(x/3)+1)/2

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inverse of f(x)=3sin(2x-1)

inverse

f (x) = 3 sin (2 x - 1)

\frac{arcsin ( \frac{x}{3} ) + 1}{2}

Solution steps

Solve for

sin (2 x - 1), y = 3 sin (2 x - 1)

sin (2 x - 1) = \frac{y}{3}

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

2 x - 1 = arcsin (\frac{y}{3})

Solve for

x, 2 x - 1 = arcsin (\frac{y}{3})

\frac{arcsin ( \frac{y}{3} ) + 1}{2}

Substitute

y = x

\frac{arcsin ( \frac{x}{3} ) + 1}{2}

What is the inverse of f(x)=3sin(2x-1) ?
The inverse of f(x)=3sin(2x-1) is (arcsin(x/3)+1)/2