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

f (x) = 2 x^{2} + 4 x - 7

f (x) = \frac{1}{2 - sin ( 3 x )}

f (x) = 12 - 2 x - \frac{3}{2}

y = x^{2} - 4 x, x \leq 0

f (x) = 2 \cdot 1 0^{x}

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