What is the inverse of y=2^{cos(x)} ?

The inverse of y=2^{cos(x)} is arccos((ln(x))/(ln(2)))

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inverse of y=2^{cos(x)}

inverse

y = 2^{c o s (x)}

arccos (\frac{ln ( x )}{ln ( 2 )})

Solution steps

Solve for

cos (x), y = 2^{c o s (x)}

cos (x) = \frac{ln ( y )}{ln ( 2 )}

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

arccos (\frac{ln ( y )}{ln ( 2 )})

Substitute

y = x

arccos (\frac{ln ( x )}{ln ( 2 )})

- \frac{1}{2} (x + 3)

\frac{x}{2 x + 3}

f (x) = 4 x + 9

f (x) = \frac{( x + 3 )}{( x - 3 )}

f (x) = 4 x + 4

What is the inverse of y=2^{cos(x)} ?
The inverse of y=2^{cos(x)} is arccos((ln(x))/(ln(2)))