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

Answer 1

To find the inverse of f(x)=log2(x) f(x) = -\log_2(x) , we swap x x and y y and then solve for y y :

x=log2(y)x = -\log_2(y)

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

2x=2log2(y)2^x = 2^{-\log_2(y)}

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

2x=1y2^x = \frac{1}{y}

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

y=12xy = \frac{1}{2^x}

Therefore, the inverse of f(x)=log2(x) f(x) = -\log_2(x) is:

f1(x)=12xf^{-1}(x) = \frac{1}{2^x}

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Answer 2

#f^-1(x)=log_2(10^{-x})#

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.

#f(x)=-log(2^x) rArr x=-log(2^{f^-1(x)})#

Step 2) Isolate the now swapped inverse function.

#-log(2^{f^-1(x)})=x#
#log(2^{f^-1(x)})=color(red)(-)x#
#2^{f^-1(x)}=color(red)(10)^-x#
#f^-1(x)=color(red)(log_2)(10^-x)#

Giving you the inverse function.

If the function is truly inverse, the original function will have been reflected along #y=x# (Which it has): graph{(y+log(2^x))(y-log(0.1^x)/log(2))=0 [-10, 10, -5, 5]}
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Answer from HIX Tutor

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.

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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