I have to solve $f(x)=x^2+2x+10$ but I'm not sure if I can solve them

Question

Given is $$ x=3 \\ h=2 \\ f(x)=x^2+2x+10 $$ what is the solution of $f(x+h)$

Is that correct? $$ f(x)=x^2+2x+10= (9+4)+2(3+2)+10 = 13+10+10 = 33 $$

Thanks in advance.

Answer 1

In the formula $$f(x) = x^2 + 2x + 10$$ think of the "$x$" as a box you get to fill in, that is, $$f(\square) = (\square)^2 + 2(\square) + 10$$ So you can put an $x$, or $x+h$, or anything you want, into the box. In particular, putting $x+h$ into the box gives you $$f(x+h) = (x+h)^2 + 2(x+h) + 10$$ Now since $x=3$ and $h=2$, you know $\boxed{x+h}=3+2=\boxed{5}$, so ... can you finish it?

Answer 2

Your basic idea is correct, but you are asked for $f(x+h)$ so that is what you should have on the left side, not $f(x)$. Then it might help to write out the function in terms of the variables first. The first term in the expression is not correct.

Answer 3

Think of the function as a black box, you throw something in, it spits something out by working its rules.

You throw $x$ in and you get $x^2+2x+10$, you throw $(x+h)$ in and you get $(x+h)^2+2(x+h)+10$, the function only transforms your number with its rule, it does not care how it is expressed.

If you know programming, you can use the concept of function there to help you understand.

function f(x) {
  console.log(`Calculating f(${x})`)
  return x * x + 2 * x + 10
}

x = 3
h = 2
console.log(f(x))
console.log(f(x+h))

Hit F12 in your browser, switch to Console, paste this in, and see the results.

Answer 4

I remember coming across stuff like $f(x)$, $p(x)$, $g(x)$, and so on, and I had no clue what any of it meant. I asked my teacher, and didn’t get a satisfactory answer. Anyway, these terms are just the mathematical way of saying that $x$ is going to be the input for the function. To make it clearer, if we have $f(x)=3x^2$, we can deduce that any input $x$ will be mapped to an output $3x^2$, under the function $f$. For example, $3$ will be mapped to $27$ under $f$, and we say $f(3)=27$. Now, in your question, $f(x)=x^2+2x+10$. The question says that $x=3$ and $h=2$. Therefore, $f(x+h)=f(3+2)=f(5)$. To find $f(5)$, simply take $5$ as the input of your function. In other words, replace each $x$ in $f(x)$ by $5$ and evaluate.