What is the inverse of f(x)=arccos(sqrt(1-x^2)) ?

The inverse of f(x)=arccos(sqrt(1-x^2)) is sqrt(-cos^2(x)+1),-sqrt(-cos^2(x)+1)

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inverse of f(x)=arccos(sqrt(1-x^2))

inverse

f (x) = arccos (1 - x^{2})

- cos^{2} (x) + 1, - - cos^{2} (x) + 1

Solution steps

arccos (a) = b \Rightarrow a = cos (b)

1 - x^{2} = cos (y)

Solve for

x, 1 - x^{2} = cos (y)

- cos^{2} (y) + 1, - - cos^{2} (y) + 1

Substitute

y = x

- cos^{2} (x) + 1, - - cos^{2} (x) + 1

What is the inverse of f(x)=arccos(sqrt(1-x^2)) ?
The inverse of f(x)=arccos(sqrt(1-x^2)) is sqrt(-cos^2(x)+1),-sqrt(-cos^2(x)+1)