Question

If f(x) = 3 ^ x, prove that f(x) + f(x + 1) = 4f (x) .

Answer 1

see explanation

Explanation:

Given

f(x) =
`3^(x)` , then

f(x + 1) =
`3^(x+1)` =
`3^(x)` × 3

Then

f(x) + f(x + 1)

=
`3^(x)` + 3.
`3^(x)` ← factor out
`3^(x)` from each term

=
`3^(x)` (1 + 3)

= 4.
`3^(x)`

= 4f(x)