What is the inverse of f(x)=3log_{e}(1+x/2) ?

The inverse of f(x)=3log_{e}(1+x/2) is e^{x/3}*2-2

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inverse of f(x)=3log_{e}(1+x/2)

inverse

f (x) = 3 lo g_{e} (1 + \frac{x}{2})

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

Solution steps

y = 3 lo g_{e} (1 + \frac{x}{2})

Replace

x

with

y

x = 3 lo g_{e} (1 + \frac{y}{2})

Solve for

y, x = 3 lo g_{e} (1 + \frac{y}{2})

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

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

10 lo g_{6} (y)

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

f (x) = x^{2} - 5 + 2

f (x) = - (x - 5) - 2

What is the inverse of f(x)=3log_{e}(1+x/2) ?
The inverse of f(x)=3log_{e}(1+x/2) is e^{x/3}*2-2