What is the inverse of f(x)= 1/3 (5)^{-2(x+4)}-1 ?

The inverse of f(x)= 1/3 (5)^{-2(x+4)}-1 is -(ln(3x+3))/(2ln(5))-4

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inverse of f(x)= 1/3 (5)^{-2(x+4)}-1

inverse

f (x) = \frac{1}{3} (5)^{- 2 (x + 4)} - 1

- \frac{ln ( 3 x + 3 )}{2 ln ( 5 )} - 4

Solution steps

y = \frac{1}{3} \cdot 5^{- 2 (x + 4)} - 1

Replace

x

with

y

x = \frac{1}{3} \cdot 5^{- 2 (y + 4)} - 1

Solve for

y, x = \frac{1}{3} 5^{- 2 (y + 4)} - 1

- \frac{ln ( 3 x + 3 )}{2 ln ( 5 )} - 4

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

f (x) = (x - 2)^{2} + 6

2 \cdot 5^{x} - 8

- 2 x - 3

f (x) = - 2 x + 11 + 12

What is the inverse of f(x)= 1/3 (5)^{-2(x+4)}-1 ?
The inverse of f(x)= 1/3 (5)^{-2(x+4)}-1 is -(ln(3x+3))/(2ln(5))-4