A.f(sin2x)= sinx b . f(sin2x)= x2+x c . f(x2+ 1)= | x+ 1 | d . f(x2+2x)= | x+ 1 |

+2x)=|x+ 1|

The question means, can you find a function that satisfies one of the above four conditions?

The answer is D.

Test Center: Solution of Analytic Function and Common Methods.

Special topic: properties and applications of functions.

Analysis: take a special value with x and judge right or wrong through the definition of the function.

Answer:

Solution:

A. if x=0, sin2x=0, ∴ f (0) = 0;

If x=π/2, then sin2x=0, ∴ f (0) =1;

∴f(0)=0 and 1, which do not conform to the definition of function;

∴ There is no function f(x), but there is f (sin2x) = sinx for any x∈R;

B. if x=0, then f (0) = 0;

If x=π, then f (0) = π 2+π; ∴f(0) has two values, which does not conform to the definition of function; ∴ This option is wrong;

C if x= 1, then f (2) = 2; If x =- 1, then f (2) = 0; So f(2) has two values, which does not conform to the definition of function; ∴ This option is wrong;

D let |x+ 1|=t, and t≥0, then f (T2-1) = t;

Let t2- 1 = x, then t = √ x+1;

∴f(x)=； =√x+ 1

That is, there exists a function f (x) = √ x+ 1, and for any x∈R, there exists f (x2+2x) = | x+1|; ∴ This choice is correct.

Therefore, choose: d.

Comments: This topic examines the application of function definition and the examination of basic knowledge, but it is more difficult to think and solve problems.