What is the inverse of f(x)=log_{3}(x-1)+4 ?

The inverse of f(x)=log_{3}(x-1)+4 is 3^{x-4}+1

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inverse of f(x)=log_{3}(x-1)+4

inverse

f (x) = lo g_{3} (x - 1) + 4

3^{x - 4} + 1

Solution steps

y = lo g_{3} (x - 1) + 4

Replace

x

with

y

x = lo g_{3} (y - 1) + 4

Solve for

y, x = lo g_{3} (y - 1) + 4

3^{x - 4} + 1

f (x) = \frac{- 5 x - 3}{- 2 x - 4}

y = 3 x - 6 + 11

3^{x + 1} - 1

f (x) = - 3 (2 + x)

f (x) = \frac{21}{x ^{2} - 25} - 3

What is the inverse of f(x)=log_{3}(x-1)+4 ?
The inverse of f(x)=log_{3}(x-1)+4 is 3^{x-4}+1