1. ## Function analysis

If g(x-1)= x^(2) + 2, then g(x)=?

Answer = x^(2) + 2x + 3

Thanks for the help

2. ## Re: Function analysis

Let's define f(x) = g(x - 1) = x^2 + 2. Then what is f(x + 1)?

3. ## Re: Function analysis

Originally Posted by benny92000
If g(x-1)= x^(2) + 2, then g(x)=?

Answer = x^(2) + 2x + 3

Thanks for the help
$\displaystyle g(x) = g(x - 1 + 1)$, so if $\displaystyle g(x - 1) = x^2 + 2$ then $\displaystyle g(x) = (x + 1)^2 + 2 = x^2 + 2x + 1 + 2 = x^2 + 2x + 3$.

4. ## Re: Function analysis

Originally Posted by Prove It
$\displaystyle g(x) = g(x - 1 + 1)$, so if $\displaystyle g(x - 1) = x^2 + 2$ then $\displaystyle g(x) = (x + 1)^2 + 2 = x^2 + 2x + 1 + 2 = x^2 + 2x + 3$.
Strictly speaking, one needs to consider g((x+1)-1): this is the result of substituting x+1 for x in the expression for g(x-1).

5. ## Re: Function analysis

Yet another approach: given g(x- 1)= x^2+ 2, let y= x- 1 so that x= y+ 1. Then g(x- 1)= g(y)= (y+ 1)^2+ 2= y^2+ 2y+ 3. And, of course, it follows that g(x)= x^2+ 2x+ 3.