Let the image of exponential function f (x) pass (2,4), find the explanatory formula of F (x) (2) and solve the inequality f (1-x) > √ (1 / 2)

Let the image of exponential function f (x) pass (2,4), find the explanatory formula of F (x) (2) and solve the inequality f (1-x) > √ (1 / 2)

Let f (x) = a ^ X be the exponential function,
So 4 = a ^ 2 and a = 2 (rounding off)
The analytic formula is f (x) = 2 ^ X
f(1-x)=2^(1-x)
So the inequality is 2 ^ (1-x) > √ (1 / 2)
That is 2 ^ (1-x) > 2 ^ (- 1 / 2)
∵a＝2＞1
∴ 1-x>-1/2
x

Given that the image of exponential function f (x) = a ^ (M-X) passes through point (1,2), then the solution set of inequality f (x) ≤ 1 / 2 is

1.0

If the exponential function f (x) passes through points (0,1), (2,1.69), then the inequality f ^ - 1 (| x |)

If the exponential function f (x) passes through points (0,1), (2,1.69), then the inequality f ^ - 1 (| x |) a = 1.3 = = > F (x) = 1.3 ^ X
F^(-1)(x)=log(1.3,x)
F^(-1)(|x|)=log(1.3,|x|)

On the inequality P: x ^ 2 + (A-1) x + A ^ 2 > = 0 and the exponential function f (x) = (2a ^ 2-A) ^ X of X,
If the proposition "the solution set of P is R or F (x) is an increasing function in R" is true, the value range of real number a is obtained

(1) The solution set of P is r, that is to say, if the quadratic inequality holds on R, the solution set: (- ∞, - 1] ∪ [1 / 3, + ∞) is obtained by Δ = (A-1) ^ 2-4a ^ 2 ≤ 0. (2) f (x) is an increasing function in R, that is, if the base of the exponential function is greater than 1, the solution set: (- ∞, - 1 / 2) ∪ (1, + ∞) is obtained by (2a ^ 2-A) > 1