What is the inverse of f(x)=5ln(((x+3))/2) ?

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

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inverse of f(x)=5ln(((x+3))/2)

inverse

f (x) = 5 ln (\frac{( x + 3 )}{2})

e^{\frac{x}{5}} \cdot 2 - 3

Solution steps

y = 5 ln (\frac{x + 3}{2})

Replace

x

with

y

x = 5 ln (\frac{y + 3}{2})

Solve for

y, x = 5 ln (\frac{y + 3}{2})

e^{\frac{x}{5}} \cdot 2 - 3

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

f (x) = \frac{8 x - 2}{x + 2}

f (x) = \frac{1}{6} x - 2

\frac{4 x}{x + 3}

F

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