What is the inverse of f(x)=sqrt(3)e^x-sqrt(3) ?

The inverse of f(x)=sqrt(3)e^x-sqrt(3) is ln((sqrt(3)(x+sqrt(3)))/3)

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inverse of f(x)=sqrt(3)e^x-sqrt(3)

inverse

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

ln (\frac{3 ( x + 3 )}{3})

Solution steps

y = 3 e^{x} - 3

Replace

x

with

y

x = 3 e^{y} - 3

Solve for

y, x = 3 e^{y} - 3

ln (\frac{3 ( x + 3 )}{3})

- \frac{7}{1 + x ^{2}}

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

y = - 29 + 5 (7 - x)

\frac{x - 4}{x + 4}

(5, 1), (1, 1)

What is the inverse of f(x)=sqrt(3)e^x-sqrt(3) ?
The inverse of f(x)=sqrt(3)e^x-sqrt(3) is ln((sqrt(3)(x+sqrt(3)))/3)