Find f+g, f-g, fg and \frac{f}{g}. Then determine the domain for each function. f(x)=3x^2-14x+16,\ g(x)=x-2

foass77W

foass77W

Answered question

2021-09-15

Find f+g, f-g, fg and fg. Then determine the domain for each function.
f(x)=3x214x+16, g(x)=x2

Answer & Explanation

Jayden-James Duffy

Jayden-James Duffy

Skilled2021-09-16Added 91 answers

Given,
f(x)=3x214x+16, g(x)=x2
To findf+g,fg,fg and fg and domain of each function.
f+g(x)=f(x)+g(x)=3x214x+16+x2=3x213x+14
fg(x)=f(x)g(x)=3x214x+16x+2=3x215x+18
fg(x)=f(x)g(x)=(3x214x+16)(x2)=3x36x214x2+28x+16x32=3x220x2+44x32
fg(x)=f(x)g(x)=3x214x+16x2,x2
Since all the functions f+g,fg and fg are polynomials.
So their domain is set of all real numbers R
However, fg is defined for all x except where its denomiantor vanishes.
It vanishes when x=2
Thus the domain of fg is (,2)(2,).

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