If f(x)=4^x, then f(x+1) - f(x) =?

Question

3 f(x)... but why? I know that's right because no matter what I substitute for x in my calculator it comes out, but I have no idea how to prove my work.

Answer 1

Hey there!

Since f(x)=4^x, then f(x+1)=4^(x+1).

Here's the answer.

f(x+1)-f(x) --> Write the problem.
4^(x+1)-4^x --> Substitute 4^(x+1) for f(x+1) and substitute 4^x for f(x).
4^x(4-1) --> Factor out 4^x.
4^x(3) --> Subtract 4 and 1.
3f(x) Substitute f(x) for 4^x, since f(x)=4^x.

So the answer is 3f(x).

Hope it helps!

Answer 2

f(x + 1) - f(x) = 4^(x + 1) - 4^x = 4*4^x - 4^x =
= (4 -1)*4^x = 3*4^x

Answer 3

f(x + 1) - f(x)
= 4^(x + 1) - 4^x
= (4^x) ( 4) - 4^x
= 4^x((4 - 1)
= 3 ( 4^(x))
= 3 f (x)

Answer 4

f(x+1) = 4 ^ (x+1) = 4 * 4^x
f(x) = 4^x

so f(x+1) - f(x) = (4 - 1) * 4^x = 3 * 4^x

Answer 5

f(x+1) - f(x) = 4^(x+1) - 4^x
= (4^x)(4^1) - 4^x = (4^x)(4) - (4^x)(1)
= (4 - 1)(4^x) = (3)(4^x) = 3f(x)