What is the inverse of f(x)=19cos(2x)+4 ?

The inverse of f(x)=19cos(2x)+4 is (arccos((x-4)/(19)))/2

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inverse of f(x)=19cos(2x)+4

inverse

f (x) = 19 cos (2 x) + 4

\frac{arccos ( \frac{x - 4}{19} )}{2}

Solution steps

Solve for

cos (2 x), y = 19 cos (2 x) + 4

cos (2 x) = \frac{y - 4}{19}

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

2 x = arccos (\frac{y - 4}{19})

Solve for

x, 2 x = arccos (\frac{y - 4}{19})

\frac{arccos ( \frac{y - 4}{19} )}{2}

Substitute

y = x

\frac{arccos ( \frac{x - 4}{19} )}{2}

What is the inverse of f(x)=19cos(2x)+4 ?
The inverse of f(x)=19cos(2x)+4 is (arccos((x-4)/(19)))/2