# How do you find the inverse of #f(x) = -log2^x#?

To find the inverse of $f(x) = -\log_2(x)$, we swap $x$ and $y$ and then solve for $y$:

$x = -\log_2(y)$

To solve for $y$, we need to isolate it. We start by exponentiating both sides with base $2$:

$2^x = 2^{-\log_2(y)}$

Using the property $a^{-\log_a(b)} = \frac{1}{b}$, we simplify:

$2^x = \frac{1}{y}$

Next, we solve for $y$ by taking the reciprocal of both sides:

$y = \frac{1}{2^x}$

Therefore, the inverse of $f(x) = -\log_2(x)$ is:

$f^{-1}(x) = \frac{1}{2^x}$

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To find the inverse of a function, there are always a few standard steps to be taken.

Step 1) Swap the function and the variable on the other side of the equation.

Step 2) Isolate the now swapped inverse function.

Giving you the inverse function.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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