Uploaded by Michele Brunetti

esercizi1

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Si risolvano le seguenti equazioni e disequazioni:
1.
x−1
x2 − 5x + 6
≤ 0;
2.
x3 − 2x + 1
≥ 0;
x+2
3.
x3 − 3x2 + 2x
< 0;
x−4
4. |x + 1| + 2x − 3 = 2;
5.
x2 − 2
≤ 1;
x
6.
x2 − 4x + 3
< 2;
x−5
|x2 − 4| + 2x
≤ 0;
x+1
√
8. x2 − 9 = x − 4;
√
9. x2 − 4x ≤ x + 3;
√
10. x2 − 5x + 6 ≥ x + 4;
r
2
3 x − 2
11.
= 1;
x
p
12. |x2 − 1| − 2 = x + 2;
√
13. x2 − 1 − x ≥ 0;
√
14. x2 − 3x + 2 ≤ x − 3;
√
15. x4 − x2 ≥ x2 − 1;
x
1
16.
< 3;
4
x x
1
1
−
+ 2 > 0;
17.
4
2
7.
18. 9x − 53̇x + 6 ≤ 0;
1
19. 2−x + 2x − 3 ≥ 0;
20. log21/3 x − 2 log1/3 x + 3 ≤ 0;
2
x −3
21. log
≥ 0;
x+1
2
x −x−2
≥ 0;
22. log1/2
x2 − 3
23. log 1 (x2 − x) ≤ 1;
3
24. log3 (x2 − 1) > 2;
25. log21 x − 4 log 1 x > 0;
2
2
Si risolvano i seguenti sistemi di disequazioni:
 x+3

≤2


 2x − 1

2


 x
>1
x2 + x
√

x2 + 2x ≤ 2




x + 1 ≤ 3
x−2
 2
x − 3x


≤0


x+1






3x − 1
≥ 1.

x






2


 x − 4x ≤ 0.
x+2
2
 x+2


≥0

log
x2



e2x − 3ex + 2 ≤ 0.
Si determini il dominio delle seguenti funzioni:
x2 − 3x √
1. f (x) =
+ x − 5;
x+1
x−3
2. f (x) = log3
;
x2 − 4
r
x
x2 + 4
+ 2
;
3. f (x) = 3 3
x −4 x −x
r
3
1
4. f (x) =
+
;
2
sin x
x −1
5. f (x) = arccos(x2 − 2x).
Si determinino il dominio e la positivitá delle seguenti funzioni:
x−3
;
1. f (x) = log 1
3
x2 − 4
√
2. f (x) = x2 − x − 2x;
3. f (x) = arcsin(x2 − x);
4. f (x) =
x2 − 1
− 1;
x+2
x−1
5. f (x) = 2 x+1 − 1.
3
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