(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)?
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(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)?
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(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)?
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(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)?
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(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)=?
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(gf)(2)=(sqrt(2))(x^2 + 1)
*notice it is the same as above..
(gf)(2)=(sqrt(2))5 --------> Answer
B.
(fog)(x)=?
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(fog)(2)=(sqrt(2)^2 + 1)
(fog)(2)=(2 + 1)
(fog)(2)=3 --------> Answer
(gof)(x)=?
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f(x)=x^2 +1
f(2)=2^2 +1
f(2)=4+1
f(2)=5
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g (f(x))= sqrt(2)
g (f(2))= sqrt(2)
g(5)= sqrt(2)
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(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!