How to solve (fog)(3) and (gof)(3)
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How to solve (fog)(3) and (gof)(3)

[From: ] [author: ] [Date: 12-06-28] [Hit: ]
(gof)(3)?-----------------------(gof)(x)=5(2x-3)(gof)(3)=5(2(3)-3)(gof)(3)=5(6-3)(gof)(3)=5(3)(gof)(3)=15 --------> AnswerB.Now for these, all you do is multiply their equations:(fg)(x)?----------------------(fg)(3)=(2x-3)(5x)(fg)(3)=(2(3)-3)(5(3))(fg)(3)=(6-3)(15)(fg)(3)=3(15)(fg)(3)=45 --------> Answer(gf)(x)?-----------------------(gf)(3)=(5x)(2x-3)*if you notice,......
(fog)(3)=2(5x)-3
(fog)(3)=2(5(3))-3
(fog)(3)=2(15)-3
(fog)(3)=27 --------> Answer

Ultimately what this does is you solve for g of x to then solve for f of x. We got this equation by substituting g(x)=5x in for x in the f(x)=2x-3 equation, you can see where the solution of g(x) is now used to solve for f(x). Now you see how it works, I will just show the math from here on.

(gof)(3)?
-----------------------
(gof)(x)=5(2x-3)
(gof)(3)=5(2(3)-3)
(gof)(3)=5(6-3)
(gof)(3)=5(3)
(gof)(3)=15 --------> Answer

B.
Now for these, all you do is multiply their equations:
(fg)(x)?
----------------------
(fg)(3)=(2x-3)(5x)
(fg)(3)=(2(3)-3)(5(3))
(fg)(3)=(6-3)(15)
(fg)(3)=3(15)
(fg)(3)=45 --------> Answer

(gf)(x)?
-----------------------
(gf)(3)=(5x)(2x-3)
*if you notice, it is the same thing above..
(gf)(3)=45 --------> Answer

2)
A.
sqrt = square root
(fg)(x)?
-----------------------
(fg)(2)=(x^2 + 1)(sqrt(2))
(fg)(2)=(2^2 + 1)(sqrt(2))
(fg)(2)=(4+1)(sqrt(2))
(fg)(2)=5(sqrt(2)) --------> Answer

(gf)(x)=?
-----------------------
(gf)(2)=(sqrt(2))(x^2 + 1)
*notice it is the same as above..
(gf)(2)=(sqrt(2))5 --------> Answer

B.
(fog)(x)=?
-----------------------
(fog)(2)=(sqrt(2)^2 + 1)
(fog)(2)=(2 + 1)
(fog)(2)=3 --------> Answer

(gof)(x)=?
-----------------------
f(x)=x^2 +1
f(2)=2^2 +1
f(2)=4+1
f(2)=5
-----------------------
g (f(x))= sqrt(2)
g (f(2))= sqrt(2)
g(5)= sqrt(2)
-----------------------
(gof)(2)= sqrt(2) --------> Answer

*It remains the same because there is nowhere in the equation g(x)= sqrt(2) to substitute your x values into, therefore, it stays the same regardless of x's value.

Hope that helps!
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