What is the inverse of cosh(3*+ln(x/2)) ?

The inverse of cosh(3*+ln(x/2)) is e^{arccosh(x)-3}*2

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inverse of cosh(3*+ln(x/2))

inverse

cosh (3 \cdot + ln (\frac{x}{2}))

e^{arccosh (x) - 3} \cdot 2

Solution steps

cosh (a) = b \Rightarrow a = arccosh (b)

3 + ln (\frac{x}{2}) = arccosh (y)

Solve for

x, 3 \cdot + ln (\frac{x}{2}) = arccosh (y)

e^{arccosh (y) - 3} \cdot 2

Substitute

y = x

e^{arccosh (x) - 3} \cdot 2

f (x) = - 5 + x, x \geq 5

4 x^{2} + 8 x + 17

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

f (x) = 0.005

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

What is the inverse of cosh(3*+ln(x/2)) ?
The inverse of cosh(3*+ln(x/2)) is e^{arccosh(x)-3}*2