Question

Math question ^^^ please help

Answer 1

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

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)

Answer:

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

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