What Is The Difference Between F And F(x)? Are They Always... - Quora

The range of the function is the set of all values that the function can take, in other words all of the possible values of y when y = f(x). So if y = x 2 , we can choose the domain to be all of the real numbers.you seem to be confused about how to evaluate or what $f(a)$ means for a given function. the function $f$ is a rule that tells what happens to something usually $x$ when the rule $f$ is applied. this is written as $f(x).$ for example $f(x) = \dfrac{1}{x}$ says that the rule $f$ is to find the reciprocal.I should not try to do this all at once. Instead, I'll break this into smaller, more manageable pieces. (I also note that this exercise uses the same function as the previous exercise, and one of the substitutions is the same, too. So I'm gonna cheat a bit and copy that exercise's result for f (x + h).)The name of the function is f; f(x) indicates applying the function to the value x and can also represent the actual value obtained by applying the function I have now specified that [math]f(x)=x[/math] is the only CONTINUOUS increasing solution to the problem. Note that you cannot choose any continuous...

algebra precalculus - Evaluate the Difference quotient...

is continuous on [a, b] and dierentiable on (a, b), and. g (x) = f (x). The Fundamental Theorem of Calculus, Part 2. The area A of the region bounded by the curves y = f (x), y = g (x), and the lines x = a, x = b, where f and g continuous and f (x) ≥ g (x) for all x in [a, b], is.2) Пусть f(x)=х² -f(x)=-х².you need the instantaneous slope. slop is rise/over run. so we take rise over run and solve for as the deltax goes to 0. so instead of f(a) we use f(x+h) to represent a point h away from x (h=deltax). 0 are 0. so we are left with. f'(x)=60x5.

Function Notation: Evaluating at an Expression | Purplemath

Home > Algebra calculators > Composite functions and Evaluating functions fog(x), f(2) calculator.Then X is called the domain of f , and Y is called the codomain of f . The element y is the image of x under f , while x is the preimage of y under f . Finally, we call range the subset of Y with preimages. Example 96. Consider the assignment rule f : X = {a, b, c} → Y = {1, 2, 3, 4} which is dened by: f = {(a...Plot the graph of f(-x) and the points at where it crosses the x and y axes by clicking on the circle below. The function definition for f(x) is below - change it and see if the things we learnt above hold for any function. The points will also move but you can change them by clicking on the arrows next to...Precalculus. Evaluate the Difference Quotient (f(x+h)-f(x))/h , f(x)=3/(x^2).

you wish to have the immediate slope. slop is rise/over run. so we take rise over run and clear up for as the deltax goes to 0. so as a substitute of f(a) we use f(x+h) to represent a point h clear of x (h=deltax).

f'(x)=lim h->Zero of (10(x+h)6-10x6)/h expand 10(x+h)6 the usage of binomial coeficients

10(x+h)=10(x6+(6choose1)x5h+(6choose2)x4h2+(6choose3)x3h3+(6choose4)x2h4+(6choose5)xh5+h6)=

10x6+60x5h+150x4h2+200x3h3+150x2h4+60xh5+10h6) plug that into the original method

lim h->0 of (10x6+60x5h+150x4h2+200x3h3+150x2h4+60xh5+10h6-10x6)/h so 10x6 can also be eliminate. then the entire phrases have a h and we will be able to cancel out an h

lim h->0 60x5+150x4h+200x3h2+150x2h3+60xh4+10h5 now that there's no h within the demominator we are not dividing via Zero anymore. so we will be able to simply without delay evaluation the limit now. all the phrases with a ha where a=/=Zero are 0. so we are left with

f'(x)=60x5

(you'll brief reduce this process some if it is allowed. you'll be able to acknowledge that there is only a h in the denominator. this implies any time period to your growth that has ha with a>=2 will likely be a 0 time period. so it's worthwhile to simply say 10(x+h)6 = 10x6 + 60hx5+.... i'd now not suggest the usage of this short hand on a take a look at though.)