BrainDen.com - Brain Teasers
• 0

# Finding a function

## Question

Find a continuous function where the following identity is true: f(2x) = 3f(x)

## Recommended Posts

• 2
25 minutes ago, plasmid said:

Sort of combining the two solutions already given

Hide contents

f(x) = C 3log2x

where C is any constant

f(2x) = C 3log2(2x) = C 31+log2x = C (3 3log2x) = 3f(x)

Spoiler

I suspect the issue with this solution is that f(x) is not defined for all x, and therefore not continuous for all x.

f(x) = 3log2(|x|)almost works, but still has a discontinuity at x = 0.

Edited by ThunderCloud
##### Share on other sites

• 1
Spoiler

I'm not too sure if this is right, but I got two possible solutions:

y=3^(log(x)/log(2))

and

y=-3^(log(-x)/log(2))

I got these two solutions by trying to make an equation where the y-value triples only when the x-value doubles, and not after each x-value.

• 1

Spoiler

f(x) = 0

##### Share on other sites

• 0

Sort of combining the two solutions already given

Spoiler

f(x) = C 3log2x

where C is any constant

f(2x) = C 3log2(2x) = C 31+log2x = C (3 3log2x) = 3f(x)

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
• ### Recently Browsing   0 members

×

• #### Activity

• Riddles
×
• Create New...