4x Which of the following represents the inverse of f(x)=4^x-1+2 A f^-1(x)=log_(4)(x-2)+1 B f^-1(x)=log_(4)(x+2)+1 C f^-1(x)=log_(4)(x-2)-1 D f^-1(x)=log_(4)(x+2)-1

To find the inverse of the function $f(x)=4^{x-1}+2$, we need to follow these steps:<br /><br />1. Replace $f(x)$ with $y$: $y=4^{x-1}+2$<br />2. Swap $x$ and $y$: $x=4^{y-1}+2$<br />3. Solve for $y$:<br /> - Subtract 2 from both sides: $x-2=4^{y-1}$<br /> - Take the logarithm base 4 of both sides: $\log_{4}(x-2)=y-1$<br /> - Add 1 to both sides: $y=\log_{4}(x-2)+1$<br /><br />Therefore, the inverse of $f(x)=4^{x-1}+2$ is $f^{-1}(x)=\log_{4}(x-2)+1$. <br /><br />So, the correct answer is A $f^{-1}(x)=log_{4}(x-2)+1$.