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

1. let f(x)=2x-3 and g(x)= 5x
A.find (fog)(3) and (gof)(3)
B.find (fg)(3) and (gf)(3)

2.let f(x)=x^2 +1 and g(x) √2
A. find (fg)(2) and (gf)(2)
B. find (fog)(2) ad (gof)(2)

1. f(x) =2x - 3 and g(x) = 5x

A. (f o g ) (3) = f (g (3))
= 2 (5x) - 3
= 10x - 3
= 10 (3) - 3
= 30 - 3
= 27 . . .answer

(g o f) (3) = 5 (2x - 3)
= 10x - 3
= 10 (3) - 3
= 30 - 3
= 27 , . .answer

B. (fg) (3) = (2x - 3) (5x)
= 10x^2 - 15x
= 10 (3)^2 - 15(3)
= 10 (9) - 45
= 90 - 45
= 45 , . .answer

(gf) (3) = (5x ) (2x - 3)
= 10x^2 - 15x
= 10 (3)^2 - 15(3)
= 10 (9) - 45
= 90 -45
= 45 , . .answer

2. f(x)=x^2 +1 and g(x) = √2

A. (fg)(2) = (x^2+1) (√2)
= (2^2 + 1) (√2)
= (4 + 1) √2
= 5√2 . . .answer

(gf)(x) = √2 (x^2 + 1)
= √2 (2^2 + 1)
= √2 ( 4 + 1)
= √2 (5)
= 5√2 , . .answer

B. (f o g) (2) = f (g (2))
= (√2)^2 + 1
= 2 + 1
=3, . . .answer

f(2) = x^2 + 1
= 2^2 + 1
= 5
(g o f)(2) = g (f (2))
= g (5)
= √5 , . .answer

1. (fog)(3)=f(5*3)=f(15)=2*15-3=27
(gof)(3)=g(2*3-3)=g(3)=5*3=15
(fog)(3) and (gof)(3) and (fg)(3) and (gf)(3) are same respectively

2. (fg)(2)=f(root2)=root2^2+1=3

.(gf)(2)=g(5)=root5

1) These are called composite functions. Also can be written as f (g(x)) for example and hopefully you understand why after this

A.
First, think of it as f of g of x. That means, your saying x=3, so you must now plug 3 in for x in the g(x)=5x equation. Anytime you have a f of g or g of f, you always do the second one first.

g(x)=5(3)
g(x)=15

So now, you will take that value, and plug it in for x in the f(x)=2x-3 equation. The answer you get here will be your answer for (fog)(3). You will see what I mean.

f(x)=2(15)-3
f(x)=30-3
f(x)=27
*Now look at it this way