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

The inverse of f(x)=4-3cos(3x-x/3) is (3arccos(-(x-4)/3))/(8)

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

inverse

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

\frac{3 arccos ( - \frac{x - 4}{3} )}{8}

Solution steps

Solve for

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

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

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

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

Solve for

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

\frac{3 arccos ( - \frac{y - 4}{3} )}{8}

Substitute

y = x

\frac{3 arccos ( - \frac{x - 4}{3} )}{8}

What is the inverse of f(x)=4-3cos(3x-x/3) ?
The inverse of f(x)=4-3cos(3x-x/3) is (3arccos(-(x-4)/3))/(8)