What is the inverse of g(x)=2^{sin(pix)} ?

The inverse of g(x)=2^{sin(pix)} is (arcsin((ln(x))/(ln(2))))/pi

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inverse of g(x)=2^{sin(pix)}

inverse

g (x) = 2^{s i n (π x)}

\frac{arcsin ( \frac{l n ( x )}{l n ( 2 )} )}{π}

Solution steps

Solve for

sin (π x), y = 2^{s i n (π x)}

sin (π x) = \frac{ln ( y )}{ln ( 2 )}

sin (a) = b \Rightarrow a = arcsin (b)

π x = arcsin (\frac{ln ( y )}{ln ( 2 )})

Solve for

x, π x = arcsin (\frac{ln ( y )}{ln ( 2 )})

\frac{arcsin ( \frac{l n ( y )}{l n ( 2 )} )}{π}

Substitute

y = x

\frac{arcsin ( \frac{l n ( x )}{l n ( 2 )} )}{π}

(x + 1)^{\frac{1}{3}}

f (x) = 1 x^{3} - 6

f (x) = \frac{1}{2} x + 2 - 1 + 4

f (x) = 1 x^{3} - 9

- 3 x^{2} + 5 x

What is the inverse of g(x)=2^{sin(pix)} ?
The inverse of g(x)=2^{sin(pix)} is (arcsin((ln(x))/(ln(2))))/pi