f(x) = ax + b is a linear function of x, where a and b are constants.
By using the fundamental theorem of Calculus. i.e. The integral of f(x) = F(x), your limits are [a,b]. Solve: F(b) - F(a). The FTC, second part, says that if f is a continuous real valued function of [a,b] then the integral from a to b of f(x)= F(b) - F(a) where F is any antiderivative of f, that is, a function such that F'(x) = f(x). Example: Evaluate the integral form -2 to 3 of x^2. The integral form -2 to 3 of x^2 = F(-2) - F(3) = -2^3/3 - 3^3/3 = -8/3 - 27/3 = -35/3
what symbol best describes the asymptote of an exponential function of the form F(x)=bx
a function y=f(x) is said to be reflexive if x=f(y). generally of the form :- y= (ax+b)/(cx-a) where a,b,c are constants. ex:- y=(3x+5)/(4x-3)
No. It may be part of notation that indicates a function, but by itself it does not mean anything and is surely not a function.
If the function is continuous in the interval [a,b] where f(a)*f(b) < 0 (f(x) changes sign ) , then there must be a point c in the interval a<c<b such that f(c) = 0 . In other words , continuous function f in the interval [a,b] receives all all values between f(a) and f(b)
F is linear when F(a+b) = F(a) + F(b) and if F(Ax) = AF(x) where A=constant
f is a piecewise smooth funtion on [a,b] if f and f ' are piecewise continuous on [a,b]
No. In general, a function f (from set A to set B) has an inverse if, for any elements a and b in A [f(a) and f(b) in B], f(a) = f(b) imples that a = b. Strictly speaking then, y = x2 does not have an inverse because each value of x2 (except 0) maps on to 2 distinct values of y. This does not accord with the definition of a function. For example, f(-2) = f(2) = 4 but -2 is not 2 so sqrt is technically NOT a function.
The letter f represents function notation, and replaces y as a variable. f(x)=ax+b is a linear function.
A function is a relationship that is one-to-one or many-to-one but not one-to-many. Thus, if a and b are in the domain of the function, then their images in the range, f(a) and f(b) MUST be equal.
For any function f(x) with domain D, if a=b is an element of D, then f(a)=f(b). (Never seen it, but is true and replaces all other properties of equality.)
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A linear function is one of the form f(x) = a*x + b where a and b are constants.
B. F. Groat has written: 'An introduction to the summation of differences of a function' -- subject- s -: Calculus
∫ f(x)/[(f(x) + b)(f(x) + c)] dx = [b/(b - c)] ∫ 1/(f(x) + b) dx - [c/(b - c)] ∫ 1/(f(x) + c) dx b ≠c