Question

A function g(x) has x-intercepts at (startfraction 1 over 2 endfraction, 0) and (6, 0). which could be g(x)?

Answer 1

If function has points (1/2,0) and (6,0) then $g(x)=2x^{2} -13x+6$

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 :

$2(x-1/2)=2x-1$

Therefore the function will be as under:

$g(x)=(x-6)(2x-1)$

$g(x)=2x^{2} -x-12x+6$

$g(x)=2x^{2} -13x+6$

Hence the function g(x) is $g(x)=2x^{2} -13x+6$.

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