What is the inverse of f(x)=3^{(x+3)-6} ?

The inverse of f(x)=3^{(x+3)-6} is (ln(x))/(ln(3))+3

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inverse of f(x)=3^{(x+3)-6}

inverse

f (x) = 3^{(x + 3) - 6}

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

Solution steps

y = 3^{x + 3 - 6}

Replace

x

with

y

x = 3^{y + 3 - 6}

Solve for

y, x = 3^{y + 3 - 6}

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

\frac{1 - 41 x}{x}

f (x) = \frac{( 3 x + 1 ) ^{2}}{2} - 4

y = 7 x^{2} - 55

y = \frac{( x ^{2} )}{8}, (x > 0)

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

What is the inverse of f(x)=3^{(x+3)-6} ?
The inverse of f(x)=3^{(x+3)-6} is (ln(x))/(ln(3))+3