Need help defining $f(x)$ recursively

Question

Been given a question and find it to be too vague to know what's going on.

The question is:

$f(x) = 2x + 2$. Define $f(x)$ recursively.

I'm just quite puzzled as there is no $f(0)$, $f(1)$ or $f(x-1)$ function to go by other than the original function.

Supposed to be in the form of $f(x-1)$.

Any help appreciated thanks.

Answer 1

If $f(x)=2x+2$, $f(x-1)=2(x-1)+2=2x$.

Therefore, $\boxed{f(x)=f(x-1)+2}$.

And, the point of recursive functions is to determine the next term off of the current term. The slope of this linear function is $2$. Therefore, you $+2$ to get the next term.

Answer 2

If $f(x) = 2x+2$, what is $f(x+1)$? Solving this should give you the recursion you are looking for.

Answer 3

In general this is pretty trivial just write out $f(x+1)-f(x)=2x+2-2(x-1)-2=2$ so you get $f(x+1)=f(x)+2$ .

You're already given $f(0)$ and $f(1)$ as they must coincide with the function at those points so $f(0)=2\cdot 0+2=2$ and $f(1)=2\cdot 1+2=4$