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

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

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inverse of 2^{sin(pix)}

inverse

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}

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

x^{2} + 2, x \leq 0

f (x) = 8 (2 x + 10)^{2} + 3, x \geq - 5

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

f (x) = \frac{( 4 x ^{2} - 3 )}{5}

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