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

Answer 1

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} ]

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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]}
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7