What is the inverse of f(x)=4-3cos(3x-pi/3) ?

The inverse of f(x)=4-3cos(3x-pi/3) is (3arccos(-(x-4)/3)+pi)/(9)

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inverse of f(x)=4-3cos(3x-pi/3)

inverse

f (x) = 4 - 3 cos (3 x - \frac{π}{3})

\frac{3 arccos ( - \frac{x - 4}{3} ) + π}{9}

Solution steps

Solve for

cos (3 x - \frac{π}{3}), y = 4 - 3 cos (3 x - \frac{π}{3})

cos (3 x - \frac{π}{3}) = - \frac{y - 4}{3}

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

3 x - \frac{π}{3} = arccos (- \frac{y - 4}{3})

Solve for

x, 3 x - \frac{π}{3} = arccos (- \frac{y - 4}{3})

\frac{3 arccos ( - \frac{y - 4}{3} ) + π}{9}

Substitute

y = x

\frac{3 arccos ( - \frac{x - 4}{3} ) + π}{9}

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

7 - 9 x

f (x) = - 5 cos (3 x)

\frac{3 + 5 x}{x}

y = 4 - x

What is the inverse of f(x)=4-3cos(3x-pi/3) ?
The inverse of f(x)=4-3cos(3x-pi/3) is (3arccos(-(x-4)/3)+pi)/(9)