What is the inverse of f(x)=3cos(pi/3 (x-5))+2 ?

The inverse of f(x)=3cos(pi/3 (x-5))+2 is (3arccos((x-2)/3))/(pi)+5

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inverse of f(x)=3cos(pi/3 (x-5))+2

inverse

f (x) = 3 cos (\frac{π}{3} (x - 5)) + 2

\frac{3 arccos ( \frac{x - 2}{3} )}{π} + 5

Solution steps

Solve for

cos (\frac{π}{3} (x - 5)), y = 3 cos (\frac{π}{3} (x - 5)) + 2

cos (\frac{π}{3} (x - 5)) = \frac{y - 2}{3}

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

\frac{π}{3} (x - 5) = arccos (\frac{y - 2}{3})

Solve for

x, \frac{π}{3} (x - 5) = arccos (\frac{y - 2}{3})

\frac{3 arccos ( \frac{y - 2}{3} )}{π} + 5

Substitute

y = x

\frac{3 arccos ( \frac{x - 2}{3} )}{π} + 5

What is the inverse of f(x)=3cos(pi/3 (x-5))+2 ?
The inverse of f(x)=3cos(pi/3 (x-5))+2 is (3arccos((x-2)/3))/(pi)+5