Q: If f-1(x)g(x) inverse then the domain of g(x) the range of f(x)?

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The fx-991MS lacks the inverse operator so the matrix inverse is not possible, Try 991Es instead

Depends on what Fx is.

The graph of the function f(x) = 4, is the horizontal line to the x=axis, which passes through (0, 4). The domain of f is all real numbers, and the range is 4.

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

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Related questions

The fx-991MS lacks the inverse operator so the matrix inverse is not possible, Try 991Es instead

fx=5x1 / 9

It is -12.8, -6.4, 0, 6.4 and 12.8

29

g(x) = x/2

y=x

Domain is the number of x values that can be used and not cause an imaginary result. Range is the number of the y values that result. In f(x)=2x-5 the range is all real numbers.

Depends on what Fx is.

OK, if you say so. That means that the range is all numbers greater than +1 .

The EPA range estimate for the 2013 Infiniti FX is 404.6 mi. in the city, 571.2 mi. on the highway.

The EPA range estimate for the 2012 Infiniti FX is 380.8 mi. in the city, 547.4 mi. on the highway.

The EPA range estimate for the 2011 Infiniti FX is 380.8 mi. in the city, 547.4 mi. on the highway.