Question

f(x) = 2x+3, find f(x+h)-f(x)

Answer 1

Recall that to evaluate a function, we have to substitute the variable by the given value, in this case, the given value is

$x+h\text{.}$

Evaluating the given function at x+h, we get:

$2(x+h)+3,$

applying the distributive law, we get:

$2x+2h+3.$

Now we subtract f(x) from the above expression

$2x+2h+3-(2x+3)\text{.}$

Simplifying the above expression, we get:

$2h\text{.}$

Answer:

$2h\text{.}$