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

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

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

inverse

f (x) = 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 )})

g (x) = \frac{x ^{3}}{8} + 16

\frac{x ^{2}}{2}

y = (x + 6)^{2}

f (x) = 4 x - 1

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