UGC NET CSE | December 2013 | Part 2 | Question: 37

Question

Let f and g be the functions from the set of integers defined by $f(x) = 2x+3$ and $g(x) =3x+2$. Then the composition of f and g and g and f is given as

• A. 6x+7, 6x+11
• B. 6x+11, 6x+7
• C. 5x+5, 5x+5
• D. None of the above

Comments

Option A, B are both correct answers. See my explanation HERE. 

Video Explanation is HERE.

Answer 1

A will be ans.

f(g) = 2(3x+2)+3= 6x+7

g(f)= 3(2x+3)+2 = 6x+11

g

Comments

Option should be B

Compostion of f and g is g o f

Composition of g and f is f o g

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Option A, B are both correct answers. See my explanation HERE. 

Video Explanation is HERE. 

Answer 2

Given f(x) = 2x + 3

g(x) = 3x + 2

(fog)(x)= f( g(x) ) 

f( g(x) ) = f(3x + 2)= 2 (3x+2) +3 = 6x + 7

(gof)(x)= g( f(x) )  

g( f(x) )  = g (2x + 3) = 3 (2x + 3) +2 = 6x +11

Hence,Option(A)6x + 7 ,6x +11.

Answer 3

A, B both are correct answers.

Detailed Explanation & Clear Concept: Composition of f and g VS g and f (Click HERE)

$f(g) = 2(3x+2)+3= 6x+7$

$g(f)= 3(2x+3)+2 = 6x+11$

The statement "Composition of f and g" is Ambiguous. It could mean $fog$ Or $gof$, depending on the author. 

Source 1: Berkeley: Composition of Functions

Source 2: Stanford: Function Composition (Slide 50)