Question

Can anyone help?
If f(x)=3^x, prove that f(x) + f(x+1)= 4f(x)

Answer 1

`f(x) = {3}^(x) \\ f(x +1) = {3}^((x + 1)) \\ f(x) + f(x + 1) \\ = {3}^(x) + {3}^((x + 1)) \\ = {(1 * 3}^(x) ) +( 3 * {3}^(x) ) \\ By \: taking \: {3}^(x) \: common, \: we \: get \\ (1 + 3) * {3}^(x) \\ = 4 * {3}^(x) \\ = 4f(x)`

• f(x)+f(x+1)=4f(x), when f(x)=3^x
• Hence proved