What is the inverse of+3-4sin(2/3 (x-1)) ?

The inverse of+3-4sin(2/3 (x-1)) is (3arcsin(-(x-3)/4))/(2)+1

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inverse of+3-4sin(2/3 (x-1))

inverse

+ 3 - 4 sin (\frac{2}{3} (x - 1))

\frac{3 arcsin ( - \frac{x - 3}{4} )}{2} + 1

Solution steps

Solve for

sin (\frac{2}{3} (x - 1)), y = + 3 - 4 sin (\frac{2}{3} (x - 1))

sin (\frac{2}{3} (x - 1)) = - \frac{y - 3}{4}

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

\frac{2}{3} (x - 1) = arcsin (- \frac{y - 3}{4})

Solve for

x, \frac{2}{3} (x - 1) = arcsin (- \frac{y - 3}{4})

\frac{3 arcsin ( - \frac{y - 3}{4} )}{2} + 1

Substitute

y = x

\frac{3 arcsin ( - \frac{x - 3}{4} )}{2} + 1

f (x) = (1 - \frac{1}{0.15 \cdot 10 + 1})

y = \frac{3 x}{2} + 3

f (x) = \frac{3}{2 + x}

f (x) = \frac{5 x - 3}{4}

lo g_{10} (2 x)

What is the inverse of+3-4sin(2/3 (x-1)) ?
The inverse of+3-4sin(2/3 (x-1)) is (3arcsin(-(x-3)/4))/(2)+1