Oxford University MAT 2016 Solved Papers

When $\mathit{x}=0,\mathit{y}=1-1=0$, so we can rule out $\left(\mathit{d}\right)$ and $\left(\mathit{e}\right)$. To work out the number of $\mathit{x}$-axis intersection points, consider ${\left(\mathit{x}-1\right)}^2=\cos \left(\mathit{\pi }\mathit{x}\right)$. The shape of these graphs means they cannot intersect 6 times (eliminating (b)). The answer cannot be (c), because we know there is a crossing point $\mathit{x}=2$, but that $\mathit{y}$ is positive when $\mathit{x}=1$. So the answer is (a).