Simple function problems, the simplest function problems

Original formula = sin2x+2 3 [(1-cos2x) 2] - 3 Note: sin2x=2sinxcosx, cos2x=1-2( sinx) 2

sin2x- 3cos2x Note; Here, the auxiliary angle is formulated as asin(wx+c)+b.

2sin(2x-π/3）

So the decreasing interval [5 12 +k , 5 6 +k ] k belongs to z) Note: The decreasing interval can be seen by drawing the image.

cosx is an even function, and if you want to make sin become cos, you need to use the induction formula, and the angle of k 2 can change.

So 2(x+w)- 3=2x+k 2 gives w=(3k +2) 12(k belongs to z).

Because w belongs to (0, 2), when k = 0, w = 6, which is in line with the topic.

When k=1, w=5 12 is in line with the topic.

k is all else that is not true.

So w = 6 or 5 12

arcsint∈[-/2，+π/2]

x∈[π/2，π]

arcsin（sinx）=π-x

Friend, please [adopt the answer], your adoption is the motivation for me to answer the question, if you don't understand, please ask. Thank you.

This one is really not difficult :

1. The function y=kx+b itself is a function, if the image expressed by the function in the coordinate system is a straight line, and the straight line is composed of an infinite number of points, which corresponds to one of the definite x or y alone, then it represents a point;

For example, if the function y=x+1 is represented in the coordinate system, it is a straight line, and if there is a definite y=1 in the coordinate system, then the corresponding x=0 is the point (0,1), which is on the straight line of y=x+1, which is also a definite solution of the function;

2. The same as the above;

3. In the same way as the above, ask again if you are not clear!

X is the same thing, with the same meaning.

The x on the right takes the same value as in parentheses.

f(2)=f(1+1)=1

The two x's are not the same.

The x on the right is the conclusion reached after the calculation of the data given in the title, when f(2), that is, x+1=2

So x is equal to 1In this case, x=1 on the right

In the same way, the element can make x+1=t, then x=t-1, then f(t)=t-1, so f(x)=x-1 f(2)=1

The vertex formula is written as y=a(x-b) 2+c, and the original form is simplified, y=(x-3) 2-17

The x-axis code royal intersection is the x value of Chi Buyan when y=0, that is, (3 + root number 17,0) and (3-root number 17,0).

As for how to solve it, I think you should know that since (1,2) is a monotonic reduction interval, that is, x=1 and 2 are extreme points, and x=1 and x=2 are substituted into f respectively'(x) = 0, and f(0) = 1 three-way simultaneous solution a, b, c

Note that this area is a monotonic de-cracking interval, so at x=etc., f'(x) is less than 0, and the positive or negative of a can be tested.

There is also a slightly easier way, which is that x=0 should be in the increase range, so f'(0)=c is greater than 0, you know.

Because for any x belongs to r, f(x) > 0

So the function image is above the x-axis, so there is no intersection.

Because any x has f(x) >0, that is, any x, f(x) cannot be equal to less than 0, so there is no focus.