What is the inverse of f(x)=2sin(3x-4)+5 ?

The inverse of f(x)=2sin(3x-4)+5 is (arcsin((x-5)/2)+4)/(3)

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inverse of f(x)=2sin(3x-4)+5

inverse

f (x) = 2 sin (3 x - 4) + 5

\frac{arcsin ( \frac{x - 5}{2} ) + 4}{3}

Solution steps

Solve for

sin (3 x - 4), y = 2 sin (3 x - 4) + 5

sin (3 x - 4) = \frac{y - 5}{2}

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

3 x - 4 = arcsin (\frac{y - 5}{2})

Solve for

x, 3 x - 4 = arcsin (\frac{y - 5}{2})

\frac{arcsin ( \frac{y - 5}{2} ) + 4}{3}

Substitute

y = x

\frac{arcsin ( \frac{x - 5}{2} ) + 4}{3}

What is the inverse of f(x)=2sin(3x-4)+5 ?
The inverse of f(x)=2sin(3x-4)+5 is (arcsin((x-5)/2)+4)/(3)