# Should I use FM (x, y) or [f (x, y)] ^ m for the M-power of a function Can it be written like the former (M is the superscript)?

## Should I use FM (x, y) or [f (x, y)] ^ m for the M-power of a function Can it be written like the former (M is the superscript)?

Both, such as the sine function SiNx with respect to X
That is, it can be expressed as sin ² x. It can also be expressed as (SiNx) ²

### The function f (x) = (m ^ 2-m-1) x ^ (m ^ 2-2m-3) is a power function and is an increasing function in X ∈ (0, + ∞). Find the analytical formula of F (x)

Should it be a subtractive function on (0, + ∞)? Otherwise, the problem will not be solved
Power function coefficient must be 1
therefore
m^2-m-1=1
m^2-m-2=0
(m+1)(m-2)=0
M = - 1 or M = 2
(0, + ∞) is a subtractive function
Then the exponent is less than zero (greater than zero if it is an increasing function)
m^2-2m-3

### Function f (x) = x power of 4 / (x power of 4 + 2) Calculate the value of F (0.1) + F (0.9)

f(x)=4^x/(4^x+2)
f(1-x)=4^(1-x)/(4^(1-x)+2)
=4/(4+2*4^x)
=2/(4^x+2)
So f (x) + F (1-x) = (4 ^ x + 2) / (4 ^ x + 2) = 1
So f (0.1) + F (0.9) = 1

### Let the function f (x) = 1 / 1 + SiNx, then its tangent equation at x = 0 is?

X = 0, f (x) = 1, that is, (0,1) is the tangent point
The derivative of F (x) is - cosx / (1 + SiNx) ^ 2, and its value at x = 0 is - 1,
According to the geometric meaning of the derivative, the slope of the tangent is - 1
From the point skew formula, the tangent equation is x + Y-1 = 0

### Mixed function equation of senior one mathematics and solution of zero point 1. Like the equation f (x) = in X + 2x-6, what should I do when I get it? The primary function and logarithmic function are mixed together. I can't take you around the corner 2. I see a lot of truth in the book, but I don't understand it. What's zero? (to be concise) what should I ask for? (also be simple)

Zero point: the abscissa of the intersection of the function and the X axis, that is, the root of the corresponding equation
According to the existence theorem of zeros, if the function is continuous on a closed interval [a, b], and f (a) * f (b)

y=x^2-4x,x>0
x=0,y=0
y=-x^2+4x,x