if f(x)=x^2+3x+5 what is f(3+h)

Having trouble with function notation? It can be a little tricky! Lemme color-code it, maybe it will make more sense to you then.

\[\Large f(\color{royalblue}{x})\quad=\quad (\color{royalblue}{x})^2+3(\color{royalblue}{x})+5\]

\[\Large f(\color{royalblue}{3+h})\quad=\quad (\color{royalblue}{3+h})^2+3(\color{royalblue}{3+h})+5\]

So we just need to multiply everything out and simplify. Understand how we plug 3+h into the function?

I'm not all that clear on how to solve these, mathmatics isn't my strong-suit.

You can kind of think of the function like this:\[\Large f(\qquad)\quad=\quad (\qquad)^2+3(\qquad)+5\] Those empty brackets are placeholders for whatever we want to plug into the function. So instead of plugging x into the function, we'll plug 3+h into each set of brackets.

\[\Large f(3+h)\quad=\quad (3+h)^2+3(3+h)+5\]

So let's deal with the easier part first, the second term. If you distribute the 3 (multiply it to each term in the brackets), what do you get? :o

you pretty much replace all the x's you see with the given value. Since it's 3+h you'd take all the x's and put 3+h. f(3+h)=3+h^2+3*3+h+5

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