Find the value of K

[Guest]

The question is, If f(x)=3^x and f(x+2)+f(x+3)+f(x+4)= kf(x), what is the value of k?

[Guest]

Do you understand that [tex]f(x+ 2)= 3^{x+2}= (3^x)(3^2)= 9(3^x)[/tex]? Do the same with f(x+ 3) and f(x+ 4) and add!

[HallsofIvy]

Since this is four to five months old: [tex]f(x)= 3^x[/tex], [tex]f(x+2)= 3^{x+ 2}= (3^x)(3^2)= 9(3^x)[/tex], [tex]f(x+ 3)= 3^{x+ 3}= (3^x)(3^3)= 27(3^x)[/tex], and [tex]f(x+ 4)= 3^{x+ 4}= (3^x)(3^4)= 81(3^x)[/tex].

So [tex]f(x+ 2)+ f(x+ 3)+ f(x+ 4)= 9(3^x)+ 27(3^x)+ 81(3^x)= (9+ 27+ 81)3^x= 117(3^x)[/tex].