一轻质杠杆可绕O点转动，在杠杆的A点和B端分别作用两个力F₁、F₂，已知OA：AB=1：2．

若F₁=12N，方向竖直向下，为使杠杆保持水平平衡，求作用在B端的力F₂的方向和最小值．

A:What are you going to do after the exams?

B:____Do you have any good ideas?

A:Yes, I want to relax myself. So I want to go on a trip.

B:Sounds great!____

A:I'd like to go somewhere interesting and exciting.

B:There is a new zoo in Jingyue, Changchun.____

A:No, I haven't. What about you?

B:____But my cousin went there last week. He told me people could watch the animals there in a more natural environment.

A:Really? That sounds interesting. Let's go to the zoo together.

B:OK. We can go there by bus tomorrow.

A:____It's not too far from here. And riding a bike is a kind of good exercise.

B: OK. I can't wait.

已知f（x）=2^x﹣1的反函数为f^﹣1（x），g（x）=log₄（3x+1）．

（1）若f^﹣1（x）≤g（x），求x的取值范围D．

（2）设函数$H\left(x\right)=g\left(x\right)-\frac{1}{2}{f}^{-1}\left(x\right)$，当x∈D时，求函数H（x）的值域．