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

The inverse of f(x)=pi-arccos(2x+1) is (cos(pi-x)-1)/2

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

inverse

f (x) = π - arccos (2 x + 1)

\frac{cos ( π - x ) - 1}{2}

Solution steps

Solve for

arccos (2 x + 1), y = π - arccos (2 x + 1)

arccos (2 x + 1) = π - y

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

2 x + 1 = cos (π - y)

Solve for

x, 2 x + 1 = cos (π - y)

\frac{cos ( π - y ) - 1}{2}

Substitute

y = x

\frac{cos ( π - x ) - 1}{2}

(1, - 1), (2, - 6)

y = x^{2} - 2 x - 24

f (x) = x^{2} - 6 x + 8

5 \frac{x}{5}

f (x) = (\frac{x}{1 + x ^{2}})

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