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\( A \) continuous function \( f(x) \) satisfying
(i) \( \mathrm{x}^{4}-4 \mathrm{x}^{2} \leq \mathrm{f}(\mathrm{x}) \leq 2 \mathrm{x}^{2}-\mathrm{x}^{3} \),
P
(ii) area bounded by \( y=f(x), y=x^{4}-4 x^{2}, y \) - axis and
W. line \( \mathrm{x}=\mathrm{t},(0 \leq \mathrm{t} \leq 2) \) is \( \mathrm{k} \) times the area bounded by \( y=f(x), y=2 x^{2}-x^{3}, y- \) axis and line \( x=t,(0 \leq t \) \( \leq 2 \) ), is given as
(a) \( f(x)=\frac{x^{4}+k x^{3}+(2 k-4) x^{2}}{1+k} \)
(b) \( f(x)=\frac{x^{4}+x^{3}+k x^{2}}{k+1} \)
(c) \( f(x)=\frac{k x^{4}-x^{3}-2 k x^{2}}{k+1} \)
(d) \( f(x)=\frac{k}{k+1}\left(x^{4}-x^{2}\right) \)
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