Find an equation for the inverse function.
-$$f ( x ) = \log ( x + 5 ) + 4$$
A) $f ^ { - 1 } ( x ) = 10 ^ { x + 4 } + 5$
B) $f ^ { - 1 } ( x ) = 10 ^ { x + 5 } + 4$
C) $f ^ { - 1 } ( x ) = 10 ^ { x - 4 } - 5$
D) $f ^ { - 1 } ( x ) = 10 ^ { x - 5 } - 4$

Question

Quizplus · Accepted Answer

To find the inverse function, we first replace $f(x)$ with $y$, getting $y = \log(x + 5) + 4$. Then we swap $x$ and $y$ to get $x = \log(y + 5) + 4$. Solving for $y$, we first subtract 4 from both sides to get $x - 4 = \log(y + 5)$. Then, we use the property that $a = \log_b(c)$ is equivalent to $b^a = c$ to solve for $y$, getting $10^{x - 4} = y + 5$. Finally, we subtract 5 from both sides to isolate $y$, resulting in $y = 10^{x - 4} - 5$, which matches option C.

Find an Equation for the Inverse Function f(x)=log⁡(x+5)+4f ( x ) = \log ( x + 5 ) + 4f(x)=log(x+5)+4

Find an Equation for the Inverse Function $f ( x ) = \log ( x + 5 ) + 4$