Problems of exponential function in grade one of senior high school The graph of function y = (1 / 3) ^ (absolute value x) is given and the monotone interval is pointed out~

Problems of exponential function in grade one of senior high school The graph of function y = (1 / 3) ^ (absolute value x) is given and the monotone interval is pointed out~

x>=0
|x|=x
y=(1/3)^x
x

Exponential function in senior one
Finding the maximum value of function y = 2 ^ (x + 2) - 3 * 4 ^ x on [- 1,0]

Using substitution method
Let 2 ^ x = t 1 / 2

The problem of exponential function in grade one of senior high school
It is known that the odd function f (x) and even function g (x) satisfy f (x) + G (x) = a ^ X. it is proved that f (2x) = 2F (x) multiplied by G (x)

f(x)+g(x)=a^xf(-x)+g(-x)=a^(-x)-f(x)+g(x)=a^(-x)f(x)+g(x)=a^xf(x)=(a^x-a^(-x))/2g(x)=(a^x+a^(-x))/2f(2x)=(a^2x-a^(-2x))/2=2*(a^x-a^x)/2*(a^x+a^(-x))/2=2f(x)g(x)