If f(x)= x^2 + 2x, what is f(x-1)? Explain please.
a) x^2 - 3
b) x^2 - 1
c)x^2 + 1
d)x ^2 + 3

Question

If f(x)= x^2 + 2x, what is f(x-1)? Explain please. 
a) x^2 - 3
b) x^2 - 1
c)x^2 + 1
d)x ^2 + 3

dayakar · Answer

just u have to do is replace x with x-1 and simplify

whpalmer4 · Answer

it might be simpler to understand this if you rewrite it slightly.

$$f(u)=u^2+2u$$is completely equivalent to your original. it is a recipe for calculating the value of the function $f$.  you take the input value (which may be a number or an algebraic expression). multiply it by itself, then add twice the input value.

if we want to find $f(x-1)$ that is the same as letting $u=x-1$ in my version:

$$f(x-1) = f(u) = u^2+2u = (x-1)^2+2(x-1)$$
Now just expand and simplify the expression $(x-1)^2+2(x-1)$ and you have your answer.

$$(x-1)^2+2x=(x-1)(x-1)+2x=x^2-x-x+1+2x-2=x^2-1$$

it might be illustrative to try plugging in an actual number or two. 

$$f(3)= u^2+2u = 3^2+2*3=9+6=15$$
but what if that $3$ was written as $3=4-1$, so we can use the $(x-1)$ form?
$$f(3)=f(4-1) = (x-1)^2+2(x-1)=x^2-1=4^2-1=15$$
same answer!