Modulus & Inequalities (id: 71eb1f326)

本题目来源于试卷: Modulus & Inequalities，类别为 IB数学

[问答题]
Let $f(x)=x^4-0.4x^3-2.85x^2+0.9x+1.35$, 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 $g(x)=\frac{2}{3}\sin (2x-1)+\frac{1}{2}$, $\frac{1}{2}-\frac{\pi }{4}\le x\le \frac{1}{2}+\frac{\pi }{4}$.
4. 1. Find an expression for g^{-1} and state its domain.
2. Solve $(f^{-1}\circ g)(x)<0.5$ .

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