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

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

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inverse of f(x)=2pi-arcsin(1-x)

inverse

f (x) = 2 π - arcsin (1 - x)

- sin (2 π - x) + 1

Solution steps

Solve for

arcsin (1 - x), y = 2 π - arcsin (1 - x)

arcsin (1 - x) = 2 π - y

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

1 - x = sin (2 π - y)

Solve for

x, 1 - x = sin (2 π - y)

- sin (2 π - y) + 1

Substitute

y = x

- sin (2 π - x) + 1

\frac{x ^{2} + x + 1}{x}

(6.8) (2.4)

x^{2} - 6 x + 8 y + y^{2} = 0

1 - x - x^{2}

h (x) = \frac{19}{x ^{2} - 3 x}

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