mat 2025 Q26Y(ii)

mat · Uk 2 marks Curve Sketching Number of Solutions / Roots via Curve Analysis
A strictly increasing linear function $f ( x )$ has the property that if $y > x$ then $f ( y ) > f ( x )$. A student claims that if $f ( x )$ and $g ( x )$ are both strictly increasing linear functions, then so is $f ( x ) \cdot g ( x )$. Is the student correct? If so, prove the student's claim. Otherwise, find a counterexample. 
A strictly increasing linear function $f ( x )$ has the property that if $y > x$ then $f ( y ) > f ( x )$.
A student claims that if $f ( x )$ and $g ( x )$ are both strictly increasing linear functions, then so is $f ( x ) \cdot g ( x )$. Is the student correct? If so, prove the student's claim. Otherwise, find a counterexample.
Paper Questions
Q26X(i) Q26X(ii) Q26X(iii) Q26X(iv) Q26X(v) Q26Y(i)(a) Q26Y(i)(b) Q26Y(ii) Q26Y(iii) Q26Y(iv) Q26Y(v) Q26Y(vi) Q27X(i) Q27X(ii) Q27X(iii) Q27X(iv) Q27X(v) Q27Y(i) Q27Y(ii) Q27Y(iii) Q27Y(iv) Q27Y(v) Q27Y(vi)