What is the inverse of f(x)=(3-2^{arccos(x)})/5 ?

The inverse of f(x)=(3-2^{arccos(x)})/5 is cos((ln(3-x*5))/(ln(2)))

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inverse of f(x)=(3-2^{arccos(x)})/5

inverse

f (x) = \frac{3 - 2 ^{a r c c o s (x)}}{5}

cos (\frac{ln ( 3 - x \cdot 5 )}{ln ( 2 )})

Solution steps

Solve for

arccos (x), y = \frac{3 - 2 ^{a r c c o s (x)}}{5}

arccos (x) = \frac{ln ( 3 - y \cdot 5 )}{ln ( 2 )}

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

cos (\frac{ln ( 3 - y \cdot 5 )}{ln ( 2 )})

Substitute

y = x

cos (\frac{ln ( 3 - x \cdot 5 )}{ln ( 2 )})

\frac{5 s + 3}{s ^{2} - 1}

f (x) = \frac{1}{2} x - \frac{3}{7}

1 + \frac{4 x}{x + 3}

f (x) = - 3 + 3 2 x + 3

f (x) = \frac{4 x}{6 x - 5}

What is the inverse of f(x)=(3-2^{arccos(x)})/5 ?
The inverse of f(x)=(3-2^{arccos(x)})/5 is cos((ln(3-x*5))/(ln(2)))