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

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

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inverse of f(x)=log_{3}(x+3)-2

inverse

f (x) = lo g_{3} (x + 3) - 2

3^{x + 2} - 3

Solution steps

y = lo g_{3} (x + 3) - 2

Replace

x

with

y

x = lo g_{3} (y + 3) - 2

Solve for

y, x = lo g_{3} (y + 3) - 2

3^{x + 2} - 3

3 + lo g_{2} (x + 4)

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

f (x) = - \frac{2}{x - 81}

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

y = \frac{9 x - 3}{9 x + 7}

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