Question

Someone please help.

Answer 1

Hi there!

$f(x)+f(x+1)=4f(x)$

There are 3 parts to this equation:

f(x)

f(x+1)

4f(x)

We must first determine these three parts separately.

1) f(x)

We're given that  $f(x)=3^x$:

⇒ $f(x)=3^x$:

2) f(x+1)

Now, we must find f(x+1). To do so, add 1 to x in the original function $f(x)=3^x$:

⇒ $f(x+1)=3^x^+^1$

3) 4f(x)

To find 4f(x), multiply the original function $f(x)=3^x$ by 4:

$4f(x)=4*3^x$:

4) Put it all together

Now, plug each of the three parts into the equation $f(x)+f(x+1)=4f(x)$:

$f(x)+f(x+1)=4f(x)$

$3^x+3^x^+^1=4*3^x\\3^x+3^x*3=4*3^x$

Factor the left side

$3^x*(1+3)=4*3^x$

Divide both sides by 3^x

$1+3=4\\4=4$

Because this equation is true, $f(x)+f(x+1)=4f(x)$ is therefore true.

I hope this helps!