5

1 Selue +he foqlowimg; Iiean Diephanhhe 'quakos; Ste (eihen {imd the #oxum & a Jenal Seluhen @h show theve a m8 ixlegek Saluh'enss) CC- 204 o 6nuF: ()...

Question

1 Selue +he foqlowimg; Iiean Diephanhhe 'quakos; Ste (eihen {imd the #oxum & a Jenal Seluhen @h show theve a m8 ixlegek Saluh'enss) CC- 204 o 6nuF: () 2x+/44 = 4#7 (G) wx+ /54 = /G0 1) 3ox+474 = 2 (iv) 4x _ 6 4 = 48

1 Selue +he foqlowimg; Iiean Diephanhhe 'quakos; Ste (eihen {imd the #oxum & a Jenal Seluhen @h show theve a m8 ixlegek Saluh'enss) CC- 204 o 6nuF: () 2x+/44 = 4#7 (G) wx+ /54 = /G0 1) 3ox+474 = 2 (iv) 4x _ 6 4 = 48



Answers

$41-44$ Find $f \circ g \circ h$
$$
f(x)=\frac{1}{x}, \quad g(x)=x^{3}, \quad h(x)=x^{2}+2
$$

Alright for this problem we are verifying that if I take the composite of F. Of G. Of X. As well as gff affects the result for both of them will come out to be exactly X. Okay so that means I'm just taking both composite. So I'm gonna start by taking F. Of G. So that's F. Of G. F. X. So G F. X. Is my inner function. So I'm gonna plug in one half X into my F. Of X. Function. So that means every time in my ffx function that I see an X. I'm gonna plug in one half X. So that's gonna be two times one half X. Multiplying those together, that gives me X. So I have verified at least half of this problem. So now I'm going to go through and I'm gonna do it for G. Of F. Of X. Okay so I'm gonna do the same process. My inner function is now ffx. So that's G. Of two X. Because fx has a function of two X. So now every time I see X. And my G fx function, I'm gonna plug in this two X. So that'll be one half times two X. Multiply those together And I get X. So I have verified that both composites come out two X.

Students. And this question we have given a function F X and G Fx. And we need to find the value of F of G. Okay, On the element X where X can be the domain of G. Okay, Because it is taking the domain of G Now, first of all, well we have three elements in G and three elements in f. So well are Find out the value of 40 for all the three elements. Okay, so first of all, we'll find out the value of F of G 04 Okay, so what is the 1st 1st element in the domain of G? So we'll find out this value. So it becomes F of G 04 Okay, Now the value of Geo four is nothing but three. So it becomes f of three and F of three is nothing but six. Right, So it becomes six. So this element, the element which comes from this, this expression the first case it becomes the domain is four and the answer is coming out to be six. Okay, now looking at the second case, the second, the second element of uh the function G. 2nd element of the function G is six. Right? It's six. So it becomes a 4G 06. And if you look at the look at the value of G. of six, it becomes four. Okay, so It becomes a 44 and if you look at the value of a 44, it is nothing but it Okay, so it is giving us it. So this element of F of G fx becomes six, coma eight. Right now, the Turkish, the third element of the domain of G, The 3rd element is given will be it's okay, So f of GF eight. So it becomes a 5G of it And the value of f of the value of Gov it is given too big to okay, so it becomes a 42 And F two is given to be four. So the answer comes out before. Now, if you look at this element, This element begins eight, Coma four. Okay, so the elements of F off gov frg contains for GOMA six, six comma eight And 8:04. Okay, so this is the correct answer, so we can see that um Second option is the correct option. Okay, that's it. Thank you.

Okay, so this time it was different after composed of t about composed of. So let's rewrite this as after proposed of Jean composed of h of X. Okay, so let's start by plugging in that h of X. That's this a square root of X and that's applied. Cheated out now. So we're gonna have of the square root of X minus phi at applying after this is going to give us the square root of X minus five to the power of four plus one.

That X is equal to X plus four and D X is equal to root in there X minus. What? So we have to find at minus de gea friends and off minus four. This can be reading is 30 difference and off minus food minus g difference and off minus four. First week of blood here that's minus four year. So minus four plus four it was toe geo and D minus four can be denied. Here. Root under minus full minus one is equal toe root under minus five. We know that route under negative is notifying. So here, that's minus four minus G minus full. It was to geo minus root under minus fire. It becomes minus root under minus five route and any getting with North defined there, so it does not at this, IM said.


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