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Homework: Unit 3 Homework Score: 0 of 2 pts 15 of 69 (14 complete2.6.VQ-2 Assigned MediaWatch the video and then solve the problem given below:Click here t0 watch t...

Question

Homework: Unit 3 Homework Score: 0 of 2 pts 15 of 69 (14 complete2.6.VQ-2 Assigned MediaWatch the video and then solve the problem given below:Click here t0 watch the_video_First find f+g, f-9, fg andThen determine the domain for each function;f(x) = 3x2 + 13x + 12,g(x) =x+3(f+g)(x) =(Simplify your answer; )

Homework: Unit 3 Homework Score: 0 of 2 pts 15 of 69 (14 complete 2.6.VQ-2 Assigned Media Watch the video and then solve the problem given below: Click here t0 watch the_video_ First find f+g, f-9, fg and Then determine the domain for each function; f(x) = 3x2 + 13x + 12,g(x) =x+3 (f+g)(x) = (Simplify your answer; )



Answers

Find the domain of the function f given by each of the following. $$ f(x)=\frac{-x}{6 x^{2}+13 x+6} $$

Finding the domain of a function means to find all the values of X for which the function is a real number. Since division by zero is undefined, we need to make sure we exclude the values of X that would make our denominator equal to zero. To do this, set the denominator equal to zero insult for the values of X zero equals three x minus 15 X squared. We can factor a greatest common factor and then solve using the principle of zero products. The greatest common factor for three x and 15 x squared is three x dividing each term by three x three x divided by three x is one negative. 15 X squared, divided by three x is negative. Five x We now have the product of two factors that, when multiplied, gives us zero. So applying the principle of zero products, we can set each factor equal to zero in salt. For X three, X equals zero and one minus five. X equals zero for our first factor. Just divide both sides by three. And we know that when X equals zero, our denominator is zero. So we need to exclude that from our domain for our second factor. Subtract one from both sides and we have negative five X equals negative one and then divide both sides by negative five. Now we know that the value went X equals 1/5. Our denominator will also be a zero, so we need to exclude that value from the domain as well. So the domain of this function is going to clued all values of X such that X is a real number and X cannot be equal to zero and X cannot be equal to 1/5.

Okay, so we want to determine earful on domain here. So it's not that here we have a rational expression. So we're gonna be undefined winners. Dominator is equal to zero. Well, in original meter, we can practice into an X minus eight times at X plus seven. Antiquities are all so we can see that X cannot be equipped to AIDS or negative seven or function is undefined, since we are division by zero. So that means our domain is all real numbers. Except for these two terms, for that's negative. Infinity up to negative seven union with negative seven to its and then union from eight to infinity.

Yeah, but the number 95 in which you need to find the domain off X plus seven over X minus three. Okay, So since this is in factional form, so X minus tree cannot be called to zero, so X cannot be called to three. So this function will be valid for all values of X except X equal to three. So domain will be minus infinity to three une in three to infinity.

Okay, so we want to find our fallen domain. So let's recall. That's since we have a rational expression, our function. It's undefined when our denominator is equal to zero. So it's fact out an X here. Okay, so this is going to give us the X cannot be equity zero or negative one. So here are domain is going to be all real numbers except 40 And they could have won. So we'll have from they go to infinity up to Darryl are actually up to negative one first and in union that with negative 1 to 0 and then union did with zero to infinity.


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