Finding a function

Whilst doing my exercises, I came across this : Find functions that satisfy

$f(x)=f(2x+1)+5$

I found out that at $x=1$ the equation doesn't hold true, but then I got stuck. Can you guys help me solving it?

#Calculus

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
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Comments

$f(x)=a-5log_{2}(x+1)$

$\Rightarrow f(2x+1)+5=a-5log_{2}(2x+2)+5$

$=a-5log_{2}(2\cdot(x+1))+5$

$=a-5log_{2}(2)-5log_{2}(x+1))+5$

$=a-5-5log_{2}(x+1))+5$

$=a-5log_{2}(x+1)$

$=f(x)$

Δrchish Ray - 2 years, 5 months ago

I think you're supposed to find functions that satisfy the equation for all values of $x$ . Regardless, think about what functions stay invariant under the various linear mappings.

A Former Brilliant Member - 2 years, 5 months ago

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this is vvvvvvvvvvvvvvvvvvvvvvvvvery easy

Nahom Assefa - 2 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$