The function $f:x\mapsto\dfrac{m}{x}+n$ satisfies $f(-1)=1\tfrac12$ and $f(2)=9$ . Find the values of $m$ and $n$ .

Model answer

m=5, n=6.5

Also accepted: m=5,n=13/2, 5 and 6.5

Explanation:

f(-1)=-m+n=\tfrac32

and

f(2)=\tfrac{m}2+n=9

. Solving simultaneously gives

m=5

n=\tfrac{13}2=6.5

Derived from ZIMSEC Pure Mathematics Paper 2, November 2025, Q5

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