First compute the function g: [tex]g(x)=f(x-h)+k\\=(-2(x-h)+7)+k\\=-2x+(2h+k+7)[/tex] Now consider the following equation: [tex]2h+k=9[/tex] The couple [tex](4,1)[/tex] is a solution of the equation. Check that: [tex]2\times4+1=8+1=9[/tex]. So the correct answer is [tex]h=4,k=1[/tex].