$g(x) = 3x^2-6x$. What is $g(x + h)$?

Question

I am really confused on what this question is asking. h isn't defined anywhere in the problem, and I am not sure how to plug in $g(x)$ if there is an unidentified variable also in the equation. Do i distribute.. or something else? Not sure! Please help

Answer 1

Just plug $x+h$ instead of $x$: $$g\left( x+h \right)=3{ \left( x+h \right) }^{ 2 }-6\left( x+h \right) $$

Answer 2

One has $$ g(x+h)=3(x+h)^2-6(x+h)=3 x^2-6x+6 h x-6 h+3 h^2=g(x)+6 h x-6 h+3 h^2. $$

Answer 3

I only can see $$g(x+h)=3(x+h)2−6(x+h)=3(x+h)(x+h−2)$$

Answer 4

$g(x+h)=3(x+h)^2−6(x+h)=3(x^2+2hx+h^2)-6x-6h=3x^2+6hx+3h^2-6x-6h$

Answer 5

Remember that a function is an operation that processes an input, and returns an output. In this case both the input and output are real numbers, but the function isn't a number; it's a rule that relates the numbers from the domain, with the numbers in the range. What this means, is that you can choose any variable to define the function. All of the following definitions mean the same thing:

$$g(x) = x^2-6x$$ $$g(t) = t^2-6t$$ $$g(r) = r^2-6r$$ $$g(\gamma) = \gamma^2-6\gamma$$ $$g(3) = 3^2-6\cdot 3$$

So to simplify the problem, try defining $g$ with a different variable name (e.g. $r$) $$g(r) = r^2-6r$$

and just substitute $r=x$ to find $g(x)$. $$g(x) = x^2 - 6x$$ Then substitute $r = x+h$ to find $g(x+h)$ $$g(x+h) = (x+h)^2-6(x+h)$$

And just to reiterate, a function isn't a number; it's what you do to a number.