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

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

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inverse of f(x)=cos(pi-x)+1

inverse

f (x) = cos (π - x) + 1

- arccos (x - 1) + π

Solution steps

Solve for

cos (π - x), y = cos (π - x) + 1

cos (π - x) = y - 1

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

π - x = arccos (y - 1)

Solve for

x, π - x = arccos (y - 1)

- arccos (y - 1) + π

Substitute

y = x

- arccos (x - 1) + π

f (x) = \frac{4 x - 5}{x - 4}

f (x) = 50 - 40 x + 15 x^{2}

8 (x + 10)

f (x) = 2 (x - 8)^{2} + 5

f (x) = \frac{5 - 2 x}{( 4 x - 2 )}

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