$$\[ \mathrm{f}(x)=x-4-\cos (5 \sqrt{x}) \quad x> 0 \]$$ (a) Show that the equation $$\(\mathrm{f}(x)=0\)$$ has a root $$\(\alpha\)$$ in the interval $$\([2.5,3.5]\)$$ (2) (b) Use linear interpolation once on the interval $$\([2.5,3.5]\)$$ to find an approximation to $$\(\alpha\)$$, giving your answer to 2 decimal places. (2)

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