What is the inverse of f(x)=log_{9}(-(x-3)/2)-1 ?

The inverse of f(x)=log_{9}(-(x-3)/2)-1 is -2*9^{x+1}+3

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inverse of f(x)=log_{9}(-(x-3)/2)-1

inverse

f (x) = lo g_{9} (- \frac{x - 3}{2}) - 1

- 2 \cdot 9^{x + 1} + 3

Solution steps

y = lo g_{9} (- \frac{x - 3}{2}) - 1

Replace

x

with

y

x = lo g_{9} (- \frac{y - 3}{2}) - 1

Solve for

y, x = lo g_{9} (- \frac{y - 3}{2}) - 1

- 2 \cdot 9^{x + 1} + 3

f (x) = - ln (x) - 1

f (x) = - \frac{1}{6} x - \frac{1}{3}

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

- \frac{x + 5}{x - 6}

5 x - 25

What is the inverse of f(x)=log_{9}(-(x-3)/2)-1 ?
The inverse of f(x)=log_{9}(-(x-3)/2)-1 is -2*9^{x+1}+3