Let a be greater than 0, f (x) = the x power of e divided by a plus the x power of E, and a is an even function on R, (1) find the value of the real number a

Let a be greater than 0, f (x) = the x power of e divided by a plus the x power of E, and a is an even function on R, (1) find the value of the real number a

f(x)=e^x/a+a/e^x
f(-x)=e^(-x)/a+a/e^(-x)=1/(a*e^x)+ae^x=f(x)=e^x/a+a/e^x
1/(a*e^x)+ae^x=e^x/a+a/e^x
Even function
So Heng is established
So the coefficients of 1 / e ^ X and e ^ X are equal
So 1 / a = a
a^2=1
a>0
a=1

Let a > 0, f (x) = [(x power of E) / a] + [A / (x power of E)] be an even function on R (1) find the value of A ⑵ prove the increasing function of F (x) on (0, + ∞)

Even function f (x) = f (- x) f (x) = e ^ X / A + A / e ^ XF (- x) = e ^ (- x) / A + A / e ^ Xe ^ X / A + A / e ^ x = e ^ (- x) / A + A / e ^ (- x) e ^ X / A + A / e ^ x = 1 / (AE ^ x) + AE ^ Xe ^ x (1 / A-A) = 1 / e ^ x (1 / A-A) 1 / a = AA = 1 or - 1A > 0, so a = 1 set 00E ^ x1e ^ x2 > 0 (e ^ x2-e ^ x1) (e ^ x1e ^ x2-1) / (e ^ x1e

Let the function f (x) = x (e ^ x + AE ^ - x) (x belongs to R) be an even function, then the value of the real number a is_____ E ^ x is the x power of E AE ^ - x is the - x power of a times E

f(-x)=f(x)
-x[(e^-x)+(ae^x)]=x(e^x+ae^-x)
Polynomials are equal, and the coefficients of the corresponding terms are equal, so a = - 1

If the function y = xa2-4a-9 is an even function and (0, + ∞) is a subtractive function, the value of a conforming to the meaning of the question is () A. 0 B. 1 C. 2 D. 4

If the function y = xa2-4a-9 is an even function, a2-4a-9 must be an even number,
When a = 0, a2-4a-9 = - 9 does not comply;
When a = 2, a2-4a-9 = - 13 is inconformity;
When a = 4, a2-4a-9 = - 9 does not comply;
When a = 1, a2-4a-9 = - 12 conforms to,
Therefore, B

Let f (x) be a differentiable function and satisfy limx → 0 [f (1) - f (1-x)] / 2x = - 1, then the slope of tangent of curve y = f (x) at point (1, f (x)) is a.2 b.-1 c.1/2 d.-2 To the process

limx→0 [f(1)-f(1-x)]/2x
=1/2limx→0 [f(1)-f(1-x)]/x
=1/2f'(1)
=-1
f'(1)=-2

(2011. Jinzhou three module) even function f (x) is derivable in (- infinity, + infinity), and f '(1) =-2, f (x+2) =f (X-2), then the slope of curve y=f (x) at point (-5, -5 (f)) tangent is (). A. 2 B. -2 C. 1 D. -1

From the derivation of F (x) in (- ∞, + ∞), the derivation of both sides of F (x + 2) = f (X-2) is obtained: F ′ (x + 2) (x + 2) ′ = f ′ (X-2) (X-2) ′, that is, f ′ (x + 2) = f ′ (X-2) ①. From F (x) as an even function, f (- x) = f (x), so f ′ (- x) (- x) ′ = f ′ (x), that is, f