Function problems are urgent, and function problems are answered

The meaning of this sentence is that there are two definitions of f(x):

First, f(x) is an even function, i.e., f(-x)=f(x);

Second: f(x) satisfies the condition: f(x)=f(|x|）。

But the problem with this problem is that if f(x) is an even function, it must satisfy f(x)=f(|).x|), but satisfying f(x)=f(|x|) is not necessarily an even function. That is, these two conditions are mutually inclusive.

It's like saying that "the natural number x is an integer", and the latter one is an integer and there is no need to restrict it.

We know that the even function satisfies f(-x)=f(x), so we will not repeat the properties of the dual function here.

Now only for f(x)=f(|x|) for analysis.

When x 0, f(-x)=f(|-x|) = f(x), which is the same as the even function.

When x 0, f(-x)=f(|-x|)=f(-x), f(-x)=f(x) cannot be pushed.

Solution: The even function satisfies f(x)=f(-x), so f(x)=f(|).x|)

That's right, if x>0 then f(x) is equal to itself, then it is equal, that is, it is true! You understand that right!

In x>0, f(x) is f(x), so there is nothing wrong with it, if not, what should f(x) be equal to? The important thing is that f(x) = f(-x), which means that the function image is symmetrical with respect to the y-axis.

If x is greater than zero, f(x) f(|x|)

If x is less than zero, f(x) f( x)=f(|x|)

So its image will be symmetrical about the y-axis.

The even function is symmetrical about the x-axis, so f(x)=f(x).

f（x）=f(|x|) only represents the even function at x<0, and greater than 0 is itself.

It should be f(x)=|x|If f(x)=f(-x), then f(x) is an even function.

y= y'= 1/(1-x) +1/(1+x^2) )y'Aftershock'= - 2x Vertical Socks (1+x 2) 2) x = 0 at y'Aftermath'=

Summary. You can send it to me.

You can send it to me.

The second big question is the two.

Solution: (1) y=kx+b

Substituting a(2,1),b(-1,-3) into y=kx+b obtains: 1=2k+b

3=-k+b

So k=4 3, b=-5 3

So y=4 3x-5 3 can be plotted.

2) When y=4 3x-5 3 intersects with the y-axis, x=0Substituting x=0 into y=4 3x-5 3 gives y=-5 3

So the intersection is (0,-5 3).

When y=4 3x-5 3 intersects the x-axis, y=0Substituting y=0 into y=4 3x-5 3 gives x=5 4

So the intersection is (5 4, 0).

If one side of the fish pond is x, the other side is 800 x

Two cases: the first case is to build a road with a length of x and a road with a width of two meters on the other side.

Then the total area y=(800 x+2)(x+4)=3200 x+2x+808 checkmark function, when 3200 x=2x, that is, x=40, y=968 The second case is to build a two-meter-wide road with a length of x, and a one-meter-wide road on the other side.

Then the total area y=(800 x+4)(x+2)=1600 x+4x+808, as above, when 1600 x=4x, that is, x=20, y=968

In summary, the minimum value of the total area occupied is 968

Let the number of trailer compartments for each guessing liquid be x, and the corresponding number of round-trips per spike per day is y, then.

y=kx+b

Substitute (4,16) and (7,10).

k=-2,b=24

So y=-2x+24

Set the number of marketing and shipping people per day to Z

z=2*xy*110=220*x(-2x+24)=440(-(x-6)^2+36)≤440*36=15840

If and only if x = 6, i.e. 6 cars should be towed at a time to make the maximum number of people operating per day 15,840.

It's too much trouble, it's so late, don't count.

f(x)=sinwx+root:3sin(wx+2)sinwx—root:3coswx

2sin(wx-π/3)

The minimum positive accompaniment period , so 2 w=

w=2f(x)=2sin(2x-π/3)

x belongs to [- 12, 2].

2x- 3 belongs to [- 2, 2 3].

The value range is noisy Kai [-2,2].

I don't know if it's right or not, let's take a test).

Workers unload the goods at a rate of 4 tons per hour, and it takes 2 days for all the goods to be unloaded.

Find out how many goods there are: 4 tons of hours * 24 hours days * 2 days = 192 tons 1 v = 192 t vt vt = 192

2 According to a typhoon 720 kilometres from the dumping site, the centre of the typhoon is moving towards the dump at a speed of 20 kilometres per hour.

Find out how many hours to arrive: t = 720 km 20 km per hour = 36 hours.

So now the goods need to be unloaded every hour.

v = 192 tons (total) 36 hours (total time) = 16 3 tons per hour and the original: 4 tons per hour.

So the difference: 16 3-4=4 3 tons per hour.

1.If there are 4*2*24=192 tons of goods to be unloaded, the relationship is v=192 t

2.First calculate the time for the typhoon to arrive at the unloading site, 720 20 = 36 hours, and substitute the result into the relation derived from (1), v'= 192 36 = 16 3 (ton-hour).

Workers at least unload more vs per hour on average than before'-v=16 3-4=t.

If a function is symmetrical with respect to x=, then for x1=; x2=;They correspond to the same function values.

Let's analyze your example, we can find that ((x+m)+(n-x) 2)=(m+n) 2; is a constant value, so there is symmetry with respect to x=.

Summary: The function is symmetrical with respect to x=m<=>f(x)=f(2m-x).

To prove that a straight line l is the axis of symmetry of a graph g, the main idea is: for a point p on g, find the symmetry point q of p with respect to l, and prove that q is also on g. Then for a point (x0, f(x0)) on the function y = f(x), first find its symmetry point about the line x = as (u,f(x0)), of course x0 + u = (m + n), so u = (m+n) -x0.

Just prove that f(u) = f(x0). Apparently there is.

f(u) = f((n-x0) +m) = f(n - n-x0)) = f(x0)