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}

f (x) = \frac{x ^{2} - 9}{2 x ^{2}}

f (x) = 9 x^{2} - 13

\frac{5 - 2 X}{4 X - 2}

f (x) = \frac{( x ^{2} - 4 )}{2 x ^{2}}

(6)^{\frac{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