What is the inverse of f(x)=10sin(x)+2 ?

The inverse of f(x)=10sin(x)+2 is arcsin((x-2)/(10))

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inverse of f(x)=10sin(x)+2

inverse

f (x) = 10 sin (x) + 2

arcsin (\frac{x - 2}{10})

Solution steps

Solve for

sin (x), y = 10 sin (x) + 2

sin (x) = \frac{y - 2}{10}

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

arcsin (\frac{y - 2}{10})

Substitute

y = x

arcsin (\frac{x - 2}{10})

What is the inverse of f(x)=10sin(x)+2 ?
The inverse of f(x)=10sin(x)+2 is arcsin((x-2)/(10))