本题目来源于试卷: Modulus & Inequalities，类别为 IB数学
[问答题]
Let $f(x)=x^{4}-0.4 x^{3}-2.85 x^{2}+0.9 x+1.35$, for x $\in \mathbb{R} $.
1. Find the solutions for f(x)>0 .
2. For the graph of y=f(x) ,
1. find the coordinates of local minimum and maximum points.
2. find the x -coordinates of the points of inflexion.
The domain of f is now restricted to [a, b] where a, b $\in \mathbb{R}^{+}$ .
3. 1. Write down the smallest value of a>0 and the largest value of b>0 for which f has an inverse. Give your answers correct to three significant figures.
2. For these values of a and b , sketch the graphs of y=f(x) and y=$f^{-1}(x)$ on the same set of axes, showing clearly the coordinates of the end points of each curve.
3. Solve f^{-1}(x)=0.5 .
Let $g(x)=\frac{2}{3} \sin (2 x-1)+\frac{1}{2}$, $\frac{1}{2}-\frac{\pi}{4} \leq x \leq \frac{1}{2}+\frac{\pi}{4} $.
4. 1. Find an expression for g^{-1} and state its domain.
2. Solve $ \left(f^{-1} \circ g\right)(x)<0.5$ .
参考答案: 
本题详细解析:
暂无
| 
