Given that f (x) is a quadratic function and f (0) = 0, f (x + 1) = f (x) + X + 1, find f (x)

Given that f (x) is a quadratic function and f (0) = 0, f (x + 1) = f (x) + X + 1, find f (x)

Given that the range of F (x) = 2x + 1 is [- 1,3], what is the domain of F (x)?
The function f (x) = 2x + 1 is an increasing function
2x1+1=f max=3
x1=1
2x2+1=f min=-1
x2=-1
The domain of F (x) is [- 1,1]
What does f (x + 4) = f (x) mean?
This equation shows that f (x) is a periodic function, and the value of point x + 4 is the same as that of X; the period of the periodic function is 4
If f (x) is an odd function over R, when x is greater than or equal to 0, f (x) = x-2x, find the expression of F (x) over R
x>=0 f(x)=x2-2x
x0 f(-x)=x2+2x f(-x)=-f(x)
f(x)=-x2-2x
We get f (x) = x2-2x x > = 0
-x2-2x x
A mathematical function f (x) in senior one!
Given f (x) = {(the first row) X-5 (x is greater than or equal to 6) and (the second row) f (x + 2) (x is less than 6), then f (3) + = () means a piecewise function. I may not describe it clearly. How much is the answer? Why
f(3)=f(3+2)=f(5)=f(5+2)=f(7)
f(7)=7-5=2
So f (3) = 2
It is known that y = f (x) is an odd function defined on R. when x > 0, f (x) = x2-2x + 2, the expression of F (x) on R is obtained
From the meaning of the question: F (- 0) = - f (0) = f (0), f (0) = 0; when x < 0, then - x > 0, because when x > 0, f (x) = x2-2x + 2, so f (- x) = - x) 2-2 (- x) + 2 = x2 + 2x + 2, and because f (x) is an odd function defined on R, so f (- x) = - f (x), so f (x) = - x2-2
If f (cosx) = cos3x, then f (SiNx)=________ Answer: (- sin3x)
If f (TaNx) = cot3x, then f (Cotx)=________ Answer: (tan3x)
f(sinx)=f[cos(90-x)]=cos(270-3x)=-sin3x,f(cotx)=f[tan(90-x)]=cot(270-3x)=tan3x.
The answers come out. What are they asking
The definition field of odd function f (x) is R. when x ≥ 0, f (x) = the square of X - 2x, then the expression of F (x) on R is
Let x = 0, f (x) = - f (- x) = - x ^ 2-2x (x = 0)
Let x < 0, then - x is greater than 0, and then it is substituted into the function of ≥ and written as a piecewise function
When x = 0, f (x) = the square of X - 2x
Simplification: (cos3x, sin3x) · (cosx, SiNx) and │ (cos3x, sin3x) + (cosx, SiNx) │ have process
1) (cos3x,sin3x)·(cosx,sinx)=cos3xcosx+sin3xsinx=cos(3x-x)=cos2x
2)│(cos3x,sin3x)+(cosx,sinx)│=|(cos3x+cosx,sin3x+sinx)|=√[(cos3x+cosx)^2+(sin3x+sinx)^2]
=√[(cos3x)^2+(sin3x)^2+2(cos3xcosx+sin3xsinx)+(sinx)^2+(cosx)^2]=√(2+2cos2x)＝√ [（2cosx）^2]=|2cosx|
F (x) = the square of X (negative infinity is less than or equal to 0)
y=x^2,(x=0
x=-√y
Inverse function y = - √ x, x > = 0