What is the inverse of f(x)=5sin(2x-3) ?

The inverse of f(x)=5sin(2x-3) is (arcsin(x/5)+3)/2

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inverse of f(x)=5sin(2x-3)

inverse

f (x) = 5 sin (2 x - 3)

\frac{arcsin ( \frac{x}{5} ) + 3}{2}

Solution steps

Solve for

sin (2 x - 3), y = 5 sin (2 x - 3)

sin (2 x - 3) = \frac{y}{5}

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

2 x - 3 = arcsin (\frac{y}{5})

Solve for

x, 2 x - 3 = arcsin (\frac{y}{5})

\frac{arcsin ( \frac{y}{5} ) + 3}{2}

Substitute

y = x

\frac{arcsin ( \frac{x}{5} ) + 3}{2}

What is the inverse of f(x)=5sin(2x-3) ?
The inverse of f(x)=5sin(2x-3) is (arcsin(x/5)+3)/2