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8_murik_8 [283]
4 years ago
8

Can Anyone Help Me

Mathematics
1 answer:
hoa [83]4 years ago
3 0
Yes it s true
A. True
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Nookie1986 [14]

(\frac{g}{f})(3)=\frac{-13}{21}\\

2/3 will not be included in the domain of g/f

Step-by-step explanation:

Given functions are:

g(x) =-2x^2+5\\f(x)=9x-6

We have to calculate (f/g)(x) first

The steps will be as follows:

(\frac{g}{f})(x)=\frac{g(x)}{f(x)}

Putting the values of functions

(\frac{g}{f})(x)=\frac{-2x^2+5}{9x-6}\\We\ have\ to\ find\ the\ value\ of\ (\frac{g}{f})(x)\ at\ 3\\So,\\(\frac{g}{f})(3)=\frac{-2(3)^2+5}{9(3)-6}\\(\frac{g}{f})(3)=\frac{-2(9)+5}{27-6}\\(\frac{g}{f})(3)=\frac{-18+5}{27-6}\\(\frac{g}{f})(3)=\frac{-13}{21}

Domain of g/f:

(\frac{g}{f})(x)=\frac{-2x^2+5}{9x-6}

The function will be undefined if the denominator is zero.

To find the domain we will put the denominator equal to zero

So,

9x-6=0\\Adding\ 6\ on\ both\ sides\\9x-6+6=0+6\\9x=6\\Dividing\ both\ sides\ by\ 9\\\frac{9x}{9}=\frac{6}{9}\\x=\frac{2}{3}

Hence, the function will be undefined on x=2/3 so 2/3 will not be included in the domain of (f/g)(x)

<u>Answer:</u>

(\frac{g}{f})(3)=\frac{-13}{21}\\

2/3 will not be included in the domain of g/f

Keywords: Domain, Operations on Functions

Learn more about functions at:

  • brainly.com/question/4767370
  • brainly.com/question/4770453

#LearnwithBrainly

8 0
3 years ago
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