What is the inverse of f(x)=3^{x+2}-4 ?

The inverse of f(x)=3^{x+2}-4 is (ln(x+4))/(ln(3))-2

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inverse of f(x)=3^{x+2}-4

inverse

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

\frac{ln ( x + 4 )}{ln ( 3 )} - 2

Solution steps

y = 3^{x + 2} - 4

Replace

x

with

y

x = 3^{y + 2} - 4

Solve for

y, x = 3^{y + 2} - 4

\frac{ln ( x + 4 )}{ln ( 3 )} - 2

f (x) = - 3 + x

f (x) = \frac{3 x - 5 + 1}{4}

2 \cdot 3 x

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

f (x) = \frac{3 x - 4}{5 x + 8}

What is the inverse of f(x)=3^{x+2}-4 ?
The inverse of f(x)=3^{x+2}-4 is (ln(x+4))/(ln(3))-2