3 The diagram shows the curve $y=\mathrm{f}(x)$, where $\mathrm{f}(x)$ is a cubic polynomial in $x$. This diagram is repeated in the Printed Answer Booklet.
(a) State the values of $x$ for which $f(x)< \frac{1}{2}$, giving your answer in set notation.
[3]
[2]
(b) On the diagram in the Printed Answer Booklet, draw the graph of $y=\mathrm{f}(-x)$.
(c) Explain how you can tell that $\mathrm{f}(x)$ cannot be expressed as the product of three real linear
[1] factors.

Answer

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Answer

Express the answer in set notation: $\boxed{\{x \mid x \in (a, b)\}}$

Steps

Step 1 ：$g(x) = f(x) - \frac{1}{2}$

Step 2 ：$g(x) = cx^3 + bx^2 + ax - \frac{1}{2}$

Step 3 ：Find the values of x for which $g(x) < 0$

Step 4 ：Express the answer in set notation: $\boxed{\{x \mid x \in (a, b)\}}$