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

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

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

inverse

f (x) = 3 lo g_{3} (x + 3) + 1

3^{\frac{x - 1}{3}} - 3

Solution steps

y = 3 lo g_{3} (x + 3) + 1

Replace

x

with

y

x = 3 lo g_{3} (y + 3) + 1

Solve for

y, x = 3 lo g_{3} (y + 3) + 1

3^{\frac{x - 1}{3}} - 3

f (x) = 2 x^{4 x}

f (x) = - 2 (x + 3)^{2} - 1

f (x) = lo g_{6} (2 x) + lo g_{6} (3)

f (x) = x^{2} - 7 x

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

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