Find the range of the function y = 4 x-3 times 2 x-3
Let 2 ^ x = t, then t > 0
y=4^x-3*2^x+3
=(2^x)^2-3*2^x+3
=t^2-3t+3…… Where t > 0
=(t-3/2)^2+3/4
Because (T-3 / 2) ^ 2 is greater than or equal to 0,
So y ≥ 3 / 4
RELATED INFORMATIONS
- 1. Find the range of y = 1 / (x-1 of 3)
- 2. Is (a ^ m) ^ n = a ^ Mn true? Why?
- 3. m. N is a non-zero natural number, m △ n = 1 1, then the greatest common factor of M and N is () A. 1B. mnC. mD. n
- 4. m. N is a non-zero natural number, m divided by n = 1.1, then the greatest common factor of M and M is?
- 5. M and N are non-zero natural numbers. If M-N = 1, then the greatest common factor of M and N is
- 6. If M and N are natural numbers and M is 8 times of N, then the greatest common factor of M and N is ()
- 7. Square of P + square of M = square of N, where p prime number, m and N are natural numbers
- 8. How many values of natural number m that make m ^ 4-m ^ 2 + 4 a complete square number? Please don't paste it from Baidu. Their method is either not good or they can't understand it. It's better to draw inferences from one instance. If it's especially good, add it to 50 points, Here's how to eat beef noodles First, let m ^ 4-m ^ 2 + 4 = k ^ 2 Then m ^ 4-m ^ 2 = k ^ 2-4, so (m ^ 2-m) (m ^ 2 + m) = (K-2) (K + 2) ① If m ^ 2 and m are not zero and are integers, then we can get m ^ 2-m = K-2 or m ^ 2 + M = K + 2 (this is actually (a + b) (a-b) = (c + D) (C-D), where ABCD is a positive integer. If you give a value, you will find that a = C and B = D at any time ② If m ^ 2 or M = 0, then K does not care about it, because in any case K will have a value that meets the conditions of the problem, so directly solving m ^ 2-m = 0 or m ^ 2 + M = 0, we can get m = 0 or plus or minus 1, because m is a natural number, so m = 0,1,2
- 9. It is known that 8m ^ 2 + 1 is a perfect square number and M is a natural number Feedback: there is something wrong with your analysis. When k = 8, K (K + 1) / 2 = 36 is a perfect square number; when k = 288, K (K + 1) / 2 = (12 * 17) ^ 2 is also a perfect square number. Why do you say "when k > = 2, K and K + 1 are mutually prime, and can't be a perfect square number, so k = 1 or K = 0"?
- 10. Satisfy m square - 3M
- 11. The range of 1 divided by x power of function 2-3 is
- 12. Function, y = (2 times 3 x power + 1) divided by (4 times 3 x power - 3)
- 13. Function, y = (2-3 of x) divided by (2-4 times 2 of x)
- 14. What is the limit of 2x + SiNx / x-sinx when x tends to positive infinity?
- 15. Find the limit of function (xarcsinxsin1 / x) / SiNx when x tends to 0
- 16. When x tends to infinity, what is the limit of function (2x SiNx) / (5x + SiNx)?
- 17. The limit of SiNx / (x ^ 2 + x) and SiNx / (x ^ 2 + X + 1) at 0 SiNx / (x ^ 2 + x) and The limit of SiNx / (x ^ 2 + X + 1) at 0
- 18. The limit of (SiNx ^ - 1 * x ^ 2) / SiNx when x approaches 0
- 19. When x tends to 90 degrees, find the limit of [(SiNx) ^ 3-2 (SiNx) ^ 2 + 1] / [sinx-1]
- 20. Limx →π (SiNx / x) and limx →1 (1 + 1 / x) ^ X are used to find the limit. The difference between these two formulas and two important limit formulas is explained