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Test: Composition Of Functions - JEE MCQ


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10 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Composition Of Functions

Test: Composition Of Functions for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Composition Of Functions questions and answers have been prepared according to the JEE exam syllabus.The Test: Composition Of Functions MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Composition Of Functions below.
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Test: Composition Of Functions - Question 1

Let f: A → B and g : B → C be one - one functions. Then, gof: A → C is

Detailed Solution for Test: Composition Of Functions - Question 1

We are given that functions f : A→B and g : B→C are both one-to-one functions.
Suppose a1, a2 ∈ A such that (gof)(a1) = (gof)(a2)
⇒ g(f(a1)) = g(f(a2)) (definition of composition) Since g is one-to-one, therefore,
f(a1) = f(a2)
And since f is one-to-one, therefore, a1 = a2
Thus, we have shown that if (gof)(a1) = (gof)(a2) then a1 = a2
Hence, gof is one-to-one function.

Test: Composition Of Functions - Question 2

If f : A → B and g : B → C be two functions. Then, composition of f and g, gof : A → C is defined a​

Detailed Solution for Test: Composition Of Functions - Question 2

A composite function is denoted by (g o f) (x) = g (f(x)). The notation g o f is read as “g of f”.
Example : Consider the functions f: A → B and g: B → C. f = {1, 2, 3, 4, 5}→ {1, 4, 9, 16, 25} and g = {1, 4, 9, 16, 25} → {2, 8, 18, 32, 50}. A = {1, 2, 3, 4, 5}, B = {16, 4, 25, 1, 9}, C = {32, 18, 8, 50, 2}.Here, g o f = {(1, 2), (2, 8), (3, 18), (4, 32), (5, 50)}.

Test: Composition Of Functions - Question 3

f: R → R is defined by  f(x) = x2 - 2x + 1. Find f[f(x)] 

Test: Composition Of Functions - Question 4

Let f: Q→Q be a function given by f(x) = x2,then f -1(9) =​

Detailed Solution for Test: Composition Of Functions - Question 4

If f : A → B such that y implies B then f-1(y) = {x implies A : f(x) = y}
Let f-1(9) = x
f(x) = 9
x2 = 9
x = +-3
Thus, f-1(9) = {-3,3}

Test: Composition Of Functions - Question 5

Let  g(x) = 1 + x – [x] and 

Then f{g(x)} for all x, is equal to:

Detailed Solution for Test: Composition Of Functions - Question 5

g(x) = 1 + x - [x]
f(x) = {-1, x<0   0, x=0    1, x>0}
f(g(x)) = f[1 + x - [x]]
= f[1 + x - 1]
= f(x)
f(g(x)) is equal to f(x) 

Test: Composition Of Functions - Question 6

If ƒ(x) = xsecx, then ƒ(0) =

Detailed Solution for Test: Composition Of Functions - Question 6

f(0)=0×sec0
f(0)=0×1
f(0)=0

Test: Composition Of Functions - Question 7

Let f = {(1, 3), (2, 1), (3, 2)} and g = {(1, 2), (2, 3), (3, 1)}. What is gof(2)?

Detailed Solution for Test: Composition Of Functions - Question 7

gof(2)=g[f(2)]
=g[1]=2

Test: Composition Of Functions - Question 8

If ƒ(x) = tan-1 x and g(x) = tan(x), then (gof)(x) =

Detailed Solution for Test: Composition Of Functions - Question 8

Test: Composition Of Functions - Question 9

If f(x) = |x| and g(x) = |5x – 2|. Then, fog =​

Detailed Solution for Test: Composition Of Functions - Question 9

 f(x) = |x|   g(x) = |5x - 2|
fog = f(g(x) = g(x) = |5x - 2|

Test: Composition Of Functions - Question 10

If f: R → R and g: R → R defined by f(x) = 2x + 3 and g(x) = x2 + 7, then the value of x for which f(g(x)) = 25 is

Detailed Solution for Test: Composition Of Functions - Question 10

f : R → R     g : R → R
f(g) : R → R
f(x) = 2x + 3      g(x2) = x2 + 7
f(g(x)) = 2g(x) + 3
f(g(x)) = 2(x2 + 7) + 3
= 2x2 + 17
As it is given f(g(x)) = 25
Comparing both the eq, we get
2x2 + 17 = 25
2x2 = 8
x = +

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