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

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

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

inverse

f (t) = 3 - 2 cos (3 x + π)

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

Solution steps

Solve for

cos (3 x + π), t = 3 - 2 cos (3 x + π)

cos (3 x + π) = - \frac{t - 3}{2}

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

3 x + π = arccos (- \frac{t - 3}{2})

Solve for

x, 3 x + π = arccos (- \frac{t - 3}{2})

\frac{arccos ( - \frac{t - 3}{2} ) - π}{3}

Substitute

t = x

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

lo g_{10} (- 1.2)

ln ((s^{2} - 1) s^{2})

x^{5} + 2

f (x) = 3 x (x - 2)

\frac{x + 2}{2 x - 1}

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