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What is the answer to F times x equals x squared minus 3?
Are you trying to solve for x? Fx = x2 - 3 x2 - Fx - 3 = 0 x2 - Fx = 3 x2 - Fx + (F/2)2 = 3 + (F/2)2 (x - F/2)2 = 3 + (F/2)2 x - F/2 = ±[ 3 + (F/2)2 ]1/2 x = F/2 ± [ 3 + (F/2)2 ]1/2
If fx equals x2 then fx-1 equals?
3
What is the inverse of fx equals 2x?
g(x) = x/2
What is the limit as x approaches 2 of 1x-22?
1(x)-22 x=2 1(2)-22=Limit Limit=2-22 Limit= -20
What is domain and range of random variable?
Let S denote the sample space underlying a random experiment with elements s 2 S. A random variable, X, is defined as a function X(s) whose domain is S and whose range is a set of real numbers, i.e., X(s) 2 R1. Example A: Consider the experiment of tossing a coin. The sample space is S = fH; Tg. The function X(s) = ½ 1 if s = H ¡1 if s = T is a random variable whose domain is S and range is f¡1; 1g. Example B: Let the set of all real numbers between 0 and 1 be the sample space, S. The function X(s) = 2s ¡ 1 is a random variable whose domain is S and range is set of all real numbers between ¡1 and 1. A discrete random variable is one whose range is a countable set. The random variable defined in example A is a discrete randowm variable. A continuous random variable is one whose range is not a countable set. The random variable defined in Example B is a continiuos random varible. A mixed random variable contains aspects of both these types. For example, let the set of all real numbers between 0 and 1 be the sample space, S. The function X(s) = ½ 2s ¡ 1 if s 2 (0; 1 2 ) 1 if s 2 [ 1 2 ; 1) is a mixed random variable with domain S and range set that includes set of all real numbers between ¡1 and 0 and the number 1. Cummulative Distribution Function Given a random variable X, let us consider the event fX · xg where x is any real number. The probability of this event, i.e., Pr(X · x), is simply denoted by FX(x) : FX(x) = Pr(X(s) · x); x 2 R1: The function FX(x) is called the probability or cumulative distribution fuction (CDF). Note that this CDF is a function of both the outcomes of the random experiment as embodied in X(s) and the particular scalar variable x. The properties of CDF are as follows: ² Since FX(x) is a probability, its range is limited to the interval: 0 · FX(x) · 1. ² FX(x) is a non-decreasing function in x, i.e., x1 < x2 Ã! FX(x1) · FX(x2): 1 ² FX(¡1) = 0 and FX(1) = 1. ² For continuous random variables, the CDF fX(x) is a unifromly continuous function in x, i.e., lim x!xo FX(x) = FX(xo): ² For discrete random variables, the CDF is in general of the form: FX(x) = X xi2X(s) piu(x ¡ xi); x 2 R1; where the sequence pi is called the probability mass function and u(x) is the unit step function. Probability Distribution Function The derivative of the CDF FX(x), denoted as fX(x), is called the probability density function (PDF) of the random variable X, i.e. fX(x) = dF(x) dx ; x 2 R1: or, equivalently the CDF can be related to the PDF via: FX(x) = Z x ¡1 fX(u)du; x 2 R1: Note that area under the PDF curve is unity, i.e., Z 1 ¡1 fX(u)du = FX(1) ¡ FX(¡1) = 1 ¡ 0 = 1 In general the probability of a random variable X(s) taking values in the range x 2 [a; b] is given by: Pr(x 2 [a; b]) = Z b a fX(x)dx = FX(b) ¡ FX(a): For discrete random variables the PDF takes the general form: fX(x) = X xi2X(s) pi±(x ¡ xi): Specifically for continuous random variables: Pr(x = xo) = FX(x+ o ) ¡ FX(x¡o ) = 0: 2
Is it generally true that limit of e to the power of fx as x tends to infinity is equal to e to the power of limit of fx as x tends to infinity?
In general, for a continuous function (one that doesn't make sudden jump - the type of functions you normally deal with), the limit of a function (as x tends to some value) is the same as the function of the limit (as x tends to the same value).e to the power x is continuous. However, you really can't know much about "limit of f(x) as x tends to infinity"; the situation may vary quite a lot, depending on the function. For example, such a limit might not exist in the general case. Two simple examples where this limit does not exist are x squared, and sine of x. If the limit exists, I would expect the two expressions, in the question, to be equal.
Rewrite fx equals 5x plus 2?
f(x)=5x+2
Is fx a function if fx equals 0 if x is a rational number and 1 if x is an irrational number?
Yes. It is a piece-wise function with the limit: lim{x->0}= 0 You graph both parts as two series of dotted lines since there are infinite rational and irrational possibilities
What is the value of fx at x-2?
That depends what the function is! Just replace every occurrence of "x" by "x-2", and do any required simplifications.
What is the inverse function of f fx equals sqrt2x-1?
3
What is the derivative of 1 divided by fx under the conditions that fx is differentiable and fx cannot be 0?
Negative the derivative of f(x), divided by f(x) squared. -f'(x) / f²(x)
How do you graph fx-x-1 3 gx-x-2 and hx -3x-1?
graph G(x)=[x]-1
