What is the inverse of f(x)=log_{3}(x+9)+2 ?

The inverse of f(x)=log_{3}(x+9)+2 is 3^{x-2}-9

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inverse of f(x)=log_{3}(x+9)+2

inverse

f (x) = lo g_{3} (x + 9) + 2

3^{x - 2} - 9

Solution steps

y = lo g_{3} (x + 9) + 2

Replace

x

with

y

x = lo g_{3} (y + 9) + 2

Solve for

y, x = lo g_{3} (y + 9) + 2

3^{x - 2} - 9

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

f (x) = \frac{2 x ^{2} - 6 x - 8}{x - 5}

41.5

f (x) = \frac{x}{x ^{2} + 9 x + 18}

f (x) = \frac{2 x + 10}{x ^{2} + 5 x}

What is the inverse of f(x)=log_{3}(x+9)+2 ?
The inverse of f(x)=log_{3}(x+9)+2 is 3^{x-2}-9