Question

how do I simplify f(x)=2x+3

Answer 1

are there more details? because f(x) is already simplified.

Answer 2

As long as you leave x as it is in the function, 2x+3 cannot be simplified algebraically, as far as I can see.

Answer 3

You can substitute in values for x in the function, from which you can evaluate an answer.

f(x) = 2x + 3, this is the function in terms of x.
If we wanted the function in terms of '1', for example, them we would substitute in '1' wherever we found 'x' in the function and evaluate.

So, f(1) =2(1) + 3
=2 + 3
=5

For this function, you could do this for any possible value and get an answer. Perhaps that's what you mean by simplify, is it?

Answer 4

sorry it says find the simplified difference quotient of the following functions and find the derivative of each function

Answer 5

The difference quotient is a more longhand way of differentiating something (finding the first derivative).

If we have a function f(x), as we do here with f(x) = 2x + 3, then the first derivative, f'(x), can be written as:

\[f'(x) = \frac{ f(x+h)-f(x) }{ h }\]

where h is just some value....we don't gave to worry about it too much here.

So, as I said previously, if f(x) = 2x + 3, then f(x + h) can be found by substituting in
'x + h' for 'x' in the function. This gives us 2(x + h) + 3, or 2x + 2h +3.

So, we can start subbing in values into the difference quotient equation above:
\[f'(x) =\frac{ (2x + 2h +3) - 3 }{ h}\]

Now, try and simplify this as much as you can in order to get the simplified difference quotient. There isn't that much you can do with it, you're answer will still contain 'x' and 'h' in it.
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In getting the first derivative of f(x) = 2x + 3, it is not as complicated. We can break it up into getting the first derivative of 2x and 3 on their own and then adding the derivatives together. So, in calculating f'(x), remember:
-The derivative of any constant value is 0.
-When differentiating, remember to 'multiply by the power of x, and then reduce this power by 1'. If the new power is 0 now, then the 'x' will disappear, as anything to the power of 0 will be 1. Good Luck! :)