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Sagot :
If function has points (1/2,0) and (6,0) then [tex]g(x)=2x^{2} -13x+6\\[/tex]
Given x-intercepts at (1/2,0)(6,0) and we have to find the function g(x)
If the x-intercepts lie at (1/2,0)(6,0) then the function has roots of 6 and 1/2. Function is a relationship between variables having value of y for each value of x. Value of x is domain and value of y is known as codomain.
If we insert x=6 or x=1/2 into the equation of g(x) we will obtain 0 as under:
g(6)=0
In order to get 0 the equation will be x-6.
In order to get 0 for root the equation will be x-1/2.
but x-1/2 does not appear in any of these but its multiples can be there :
[tex]2(x-1/2)=2x-1[/tex]
Therefore the function will be as under:
[tex]g(x)=(x-6)(2x-1)[/tex]
[tex]g(x)=2x^{2} -x-12x+6[/tex]
[tex]g(x)=2x^{2} -13x+6[/tex]
Hence the function g(x) is [tex]g(x)=2x^{2} -13x+6[/tex].
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