1. If f (x) = x- 1x+ 1, then f (2) = f(2)=.

a . 1b . 12c . 13d . 14

The analytic f (2) = 2-12+1=13.x.

Answer c

2. The following groups of functions, said the same function is ().

A.y = x- 1，y = x2- 1x+ 1。

B.y = x0 and y = 1

C.y = x2，y = (x+ 1) 2。

D.f(x)=？ x？ 2x and g (x) = x? x？ 2

In analysis a, the domain of Y = X- 1 is r, while the domain of Y = X2- 1x+ 1 is {x | x ≠1};

The function y = x0 in b defines the domain {x|x≠0}, while y = 1 defines the domain as r;

The analytical expressions of the two functions in C are different;

The domains of f(x) and g(x) in d are both (0, +∞), and after simplification, F (x) = 1 and G (x) = 1, so they are the same function.

Answer d

3. Fill the bottle with water in the shape shown in Figure 2-2- 1 at a fixed speed, and the relationship between the water surface height h and the time t is ().

Figure 2-2- 1

It is analyzed that the height h of water surface increases with the increase of time t, and the increasing speed is faster and faster.

Answer b

4. The domain of the function f (x) = x- 1x-2 is ().

A.

D ..

answer

7. The domain of the function y = 3 1-x- 1 is _ _ _ _ _.

In order for the function to be meaningful, the independent variable x must satisfy

x- 1≥0 1-x- 1≠0

Solution: x≥ 1 and x≠2.

The domain of ∴ function is [1, 2)∞(2, +∞).

Answer [1, 2)∩(2, +∞)

8. Let the function f (x) = 4 1-x, if f (a) = 2, the real number A = _ _ _ _ _ _

If f (a) = 2, it is 4 1-a = 2 and the solution is a =- 1.

Answer-1

Third, answer questions.

9. The function f (x) = x+ 1x is known.

Find the domain of (1) function f(x);

(2) the value of f (4).

The solution (1) is x≥0, x≠0, x >；; 0, so the domain of the function f(x) is (0,+∞).

(2)f(4)= 4+ 14 = 2+ 14 = 94。

10. Find the domain of the following function:

( 1)y =-x2 x2-3x-2； (2)y=34x+83x-2。

For the solution that (1) makes y =-x2x2-3x-2 meaningful, it must be -x ≥ 0, 2x2-3x-2 ≠ 0, and the solution is x≤0, x ≦- 12.

Therefore, the domain of the function is {x|x≤0, x≦- 12}.

(2) In order to make y = 34x+83x-2 meaningful,

Must be 3x-2 >；; 0, namely x & gt23,

Therefore, the domain of the function is {x | x >；; 23}.

1 1. It is known that f (x) = x2 1+x2, x∈R,

(1) Calculate the value of f (a)+f (1a);

(2) Calculate the value of f (1)+f (2)+f (12)+f (3)+f (13)+f (4)+f (14).

Solution (1) Because F (a) = A2 1+A2, f (1a) =1+a2,

So f (a)+f (1A) = 1.

(2) Method 1 is because f (1) =121+12 =12, and f (2) = 221+22 = 12? 2 1+? 12? 2= 15，f(3)=32 1+32=9 10，f( 13)=？ 13? 2 1+? 13? 2= 1 10，f(4)= 42 1+42 = 16 17，f( 14)=？ 14? 2 1+? 14? 2= 1 17,

So f (1)+f (2)+f (12)+f (3)+f (13)+f (4)+f (14) =12.

Method 2 (1) shows that f (a)+f (1a) = 1, then f (2)+f (12) = f (3)+f (13).

And f (1) = 12, so f (1)+f (2)+f (12)+f (3)+f (13)+f (4)+.