in-8-13-the-domain-of-fx4-2-x-and-of-gxx2-is-the-set-of-real-numbers-and-the-domain-of-hxfrac1x-is-3

Question

In $8-13$ , the domain of $f(x)=4-2 x$ and of $g(x)=x^{2}$ is the set of real numbers and the domain of $h(x)=\frac{1}{x}$ is the set of non-zero real numbers.
a. Write each function value in terms of $x$ .
b. Find the domain of each function. 
$(\mathrm{gh})(x)$

Finian Lickona · Accepted Answer

so for this exercise were given that G of X equals X squared and h of X equals one over X and we&#x27;re required to find the expression g times h of X in terms of X and then we have to find the domain of that. So this is pretty straightforward. We just multiply g and h together. So we have X squared times one over X one of these X&#x27;s cancels, and we&#x27;re just left with G of h of X equals X. So that&#x27;s G of h of X written in terms of X. And as we can see, there are no restrictions on the value X come take for this particular expression. Um, for this h of X right here there is a restriction Ex cannot take on the value zero. Otherwise, the function is undefined. But because the X and the denominator was eliminated in this computation and we just haven&#x27;t x term, there is no restriction on the values it can take stood. That s o the domain is all for real numbers. Okay,

Finian Lickona · Answer

All right. So for this exercise, we are given that f of X equals four minus two x and G of X equals X squared. And the first thing we have to do is right. Each function in terms of X and the right, the expression g of f of X in terms of X. So this is really just going to our involve adding the two functions together, which is pretty straightforward. G ve expos f of X is just gonna be X squared minus two X plus four. And we need next. We need to determine the domain of each function. So, um, there is no restriction on the value that ex contain HQ for this function. So the domain is really just going to be all riel numbers, okay?

Finian Lickona · Answer

So for this exercise, we are given that half of X equals four minus two X g of X equals X squared, and we need to find the expression G plus three f of X in terms of X, So this is gonna be pretty straightforward. All we have to do is multiply ActiveX by three and then added to G of X. So three f of X is going to be equal to 12 minus six x and then we just add plus g of x. So that&#x27;s gonna be our final expression. G plus three f of X equals X squared minus six X plus 12. And there is no restriction on the values ex con. Taking this expressions of the domain is all real numbers.

Ashley High · Answer

in this problem. F of X is three x squared plus two X minus eight and then G of X is X plus two. It wants us to find negative f of eggs, plus four times Geum IX. Okay, so we&#x27;re gonna do negative times our whole FX mention so three X squared plus two X minus eight. We&#x27;re gonna add four times our G m X function X plus two. So we&#x27;re gonna be distributing this negative toe all three terms into this for trouble terms over here. So want to do that? This negative pretty much just changes all the signs. So this is negative three X squared, minus two X plus eight plus for X and then four times two is eight. Now let&#x27;s combine our like terms. So we have a negative two eggs and a positive for here. We haven&#x27;t ate in a eight here, So now my extraction is going to be negative. Three X squared. Negative two X plus four x will give me a positive to x eight plus eight is a positive 16. So we have negative through X squared plus two x plus 16 the domain on this. So since This is a quadratic. It is a quadratic and it is upside down. But the domain is still all real numbers. There&#x27;s no limitations on the exes that I could that I cannot put inside this auction.

Vishal Parmar · Answer

people severely, however, rational function and for the rest of function denominator cannot be for 20 So to find the undefined points, take expert minus for that is our the Internet. That isn&#x27;t good to see you. Right. So here we can. Victor out X plus two, murdered by by X minus two. That is equal to zero. But you&#x27;re express. Do that is equal to zero and X minus two. That is equal to zero. So our first undefined point is minus two and 2nd 1 is to so these are the undefined points. So the domain of the function that is minus infinity to minus two union minus do do do you and you include doing tonight, right? Thank you.

Vishal Parmar · Answer

Okay, so here we have a restaurant function and for the rest of function year, do you know miniter cannot be equal to zero? So to find the undefined points, take the normally a very quiet zero severe. You know, mandatories X minus one. So take X minus one is equal to zero. That gives an exit equal toe once. And that is the or undefined point. Right? So the domain of the function that is negative and finally toe one Union one. Great. My name. Thank you.

Problem

In $8-13$ , the domain of $f(x)=4-2 x$ and of $g(…

Problem 10 Easy Difficulty

In $8-13$ , the domain of $f(x)=4-2 x$ and of $g(x)=x^{2}$ is the set of real numbers and the domain of $h(x)=\frac{1}{x}$ is the set of non-zero real numbers.
a. Write each function value in terms of $x$ .
b. Find the domain of each function.
$(\mathrm{gh})(x)$

Answer

a) $(g h)(x)=x$
b) $\mathbb{R}$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Grace H.

Heather Z.

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Absolute Value - Example 1

Absolute Value - Example 2

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a) $(g h)(x)=x$b) $\mathbb{R}$

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Ann Xavier GantertAlgebra 2 and Trigonometry

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a) $(g h)(x)=x$
b) $\mathbb{R}$

Ann Xavier Gantert

Algebra 2 and Trigonometry