What is the inverse of 3/2 cos(5x-pi/4) ?

The inverse of 3/2 cos(5x-pi/4) is (4arccos((2x)/3)+pi)/(20)

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inverse of 3/2 cos(5x-pi/4)

inverse

\frac{3}{2} cos (5 x - \frac{π}{4})

\frac{4 arccos ( \frac{2 x}{3} ) + π}{20}

Solution steps

Solve for

cos (5 x - \frac{π}{4}), y = \frac{3}{2} cos (5 x - \frac{π}{4})

cos (5 x - \frac{π}{4}) = \frac{2 y}{3}

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

5 x - \frac{π}{4} = arccos (\frac{2 y}{3})

Solve for

x, 5 x - \frac{π}{4} = arccos (\frac{2 y}{3})

\frac{4 arccos ( \frac{2 y}{3} ) + π}{20}

Substitute

y = x

\frac{4 arccos ( \frac{2 x}{3} ) + π}{20}

f (x) = (3 x + 4)^{2}

f (x) = 5 ln (\frac{( x + 2 )}{3})

f (x) = \frac{( 2 x - 5 )}{( x + 7 )}

f (x) = 3 x + 6

What is the inverse of 3/2 cos(5x-pi/4) ?
The inverse of 3/2 cos(5x-pi/4) is (4arccos((2x)/3)+pi)/(20)