Plugging might be a safe option if you are not familiar with polynomials.

The logical way mentioned here is:

given \(f(cx)=cf(x)\) where \(f(x)\) is a polynomial say \(f(x)= a_nx^n + a_{n-1}x^{n-1}.....+ a_1x + a_0\)

So \(f(cx)=a_n(cx)^n + a_{n-1}(cx)^{n-1}.....+ a_1cx + a_0\)

Here \(f(cx)=cf(x)\) if all coeffecients except \(a_1\) is 0 i.e a linear function or all coeffecients excepts \(a_0\) is 0 i.e. a constant function.

Since the options have only one linear function we can safely say that is the correct answer.

_________________

Sandy

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