What is the inverse of f(x)=2sin(x+pi)-1 ?

The inverse of f(x)=2sin(x+pi)-1 is arcsin((x+1)/2)-pi

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inverse of f(x)=2sin(x+pi)-1

inverse

f (x) = 2 sin (x + π) - 1

arcsin (\frac{x + 1}{2}) - π

Solution steps

Solve for

sin (x + π), y = 2 sin (x + π) - 1

sin (x + π) = \frac{y + 1}{2}

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

x + π = arcsin (\frac{y + 1}{2})

Solve for

x, x + π = arcsin (\frac{y + 1}{2})

arcsin (\frac{y + 1}{2}) - π

Substitute

y = x

arcsin (\frac{x + 1}{2}) - π

What is the inverse of f(x)=2sin(x+pi)-1 ?
The inverse of f(x)=2sin(x+pi)-1 is arcsin((x+1)/2)-pi