Expressing a function with an analytic method, what is a function analytic method?

1) Knowing that the quadratic function f(x) satisfies f(2x+1)=4x-6x+5, find f(x) t = 2x +1 ==> x = (t -1) 2 f(2x+1)=4x-6x+5 ==> f(t) = 4* [t-1) 2] 2 - 6 * t-1) 2 +5 ==> f(t) = (t-1) 2 - 3(t-1) +5 ==> f(t) = t 2 - 2t +1 - 3t + 3 +5 ==> f(t) = t 2 - 5t + 9 f(x) = x 2 - 5x + 9 (2) known function f(x+1 x) = x+1 x, find f(x) f(x +1 x) = x 2 + 1 x 2 = (x + 1 x) 2 - 2 t = x +1 x f(t) = t 2 - 2 f(x) = x 2 - 2

Order 2x+|=t, so x=(t-|.)2, and then substitute this equation into the equation to get the f(t) equation, and then write t as x; In the same way, let x+1 x=t, so f(t)=t 2-2, i.e. f(x)=x 2-2

Trouble, thanks!

In mathematics, the method of expressing a function or arbitrary mathematical object analytically is called analytical.

The first thing to understand is that a function is a correspondence that occurs between sets. Then, it is necessary to understand that there is more than one function relationship between a and b. Finally, it is important to understand the three elements of a function.

The correspondence of functions is usually expressed in analytical, but a large number of functional relations cannot be expressed analytically, and can be expressed in images, ** and other forms.

As follows:

Complex variable function, fiber foci refers to the complex number as the independent variable and the stupid dependent variable of the function, and the related theory is the complex variable function theory. Analytic function is a class of functions with analytic properties in complex variable functions, and complex variable function theory is mainly to study analytic functions in complex number fields, so it is often called complex variable function theory as analytic function theory.

Origin. The concept of complex numbers originates from finding the root of an equation, and in the root finding of quadratic and cubic algebraic equations, there is a situation where bending and vertically accompany the square of negative numbers. For a long time, people didn't understand these kinds of numbers.

But with the development of mathematics, the importance of such numbers has become increasingly apparent.

Function analytic method is a general term for the method of using functions to construct a model and then cut the optimal solution.

The analysis method of many problems in economics is to use the function analysis method, such as the Hicks function: for a given (of various goods) ** and income, the demand for various goods that can maximize the utility of consumers is a (vector) function of ** and income. Correspondingly, the maximum utility that can be achieved is also a function of income and income, which is the indirect utility function.

For a given ** and utility, the demand for various goods that can enable consumers to minimize their expenditure, that is, the Hicks demand function, which is the (vector) function of ** and utility. Correspondingly, the smallest expenditure that can be achieved is also a function of ** and utility, which is the expenditure function.

The method of expressing a function analytically is called analytical.

Proportional function y=kx (k≠0).

Inverse proportional function y=k x (k≠0).

Primary function y=kx+b (k≠0).

Quadratic function y=ax +bx+c (a≠0) exponential function y=a x (a>0, and a≠1) logarithmic function y=loga x (a>0 and a≠1) power function y=x

Trigonometric function y=sinx y=cosx y=tanx