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Question 12: The value of f∘g∘h(9) could be, if 

f(x) = 1/x
g(x) = 1/(x-2)
h(x) = √x 

A. 3

B. 1/3

C. -5

D. None of these 

Answer. None of these 

Explanation.

fogoh(9) means f(g(h(9)))
Start by solving h(9) = √9 = 3 and not (3, -3) as square root of a number is always positive.
Taking the value to be 3, g(3) = 
1/(3-2) = 1 ⇒ f(1) = 1

The question is "What is value of f∘g∘h(9) could be?"

Hence the answer is "None of these are identical"

Choice D is the correct answer.

Question 13: For this question, assume the following operators: 
A*B = A2 - B2 

A-B = A/B

A+B = A * B 

A/B = A+B 

Which of the following expression would yield the result as x subtracted by y? 

A. (x*y)-(x+5)

B. (x/y)*(x-y)

C. (x*y)-(x/y)

D. (x+y)*(x-y)

Answer. (x*y)-(x/y)

Explanation.

Never solve each expression. Solve by assigning values of x and y
Let x = 6, y = 2 Therefore, required x – y = 4
x*y = 62 – 22 = 32 

x-y = 6/2 = 3

x+y = 6 * 2 = 12 

x/y = 6+2 = 8

a) 32-12 = 32/12 not equal to 4 

b) 8*3 = 82 - 32 = 55 not equal to 4 

c) 32 - 8 = 32/8 = 4

d) 12*3 = 122 - 32 not equal to 4 

The question is "Which of the following expression would yield the result as x subtracted by y?" 

Hence the answer is "(x*y) - (x/y)"

Choice C is the correct answer. 

Question 14: Find the domain of: Algebra: Functions Questions - 2 | General Test Preparation for CUET

A. (-∞,9)

B. [-1,9)

C. [-1,9) excluding 0

D. (-1,9)

Answer. (-1,9)

Explanation.

In the expression,
9-x > 0
⇒ x < 9
Also, 1-log ( 9-x) ≠ 0
⇒ log (9 – x) ≠ 1
⇒ 9-x ≠ 10
⇒ x ≠ -1
And, x + 1 > 0
⇒ x > -1

The question is "Find the domain of: Algebra: Functions Questions - 2 | General Test Preparation for CUET

Hence the answer is "(-1,9)"

Choice D is the correct answer.

Question 15: If [X] – Greatest integer less than or equal to x. Find the value of 
[√1] + [√2] + [√3] +……………………………………………………+ [√100] 

A. 615

B. 625

C. 5050

D. 505

Answer. 625

Explanation.

As can be seen, 
Thus, the series becomes:
3 * 1 + 5 * 2 + ……………………………………+ 19 * 9 + 10
 ∑(2n+1)n + 10 (where, n = 1 to 9)
 ∑2n2 + ∑n + 10

Algebra: Functions Questions - 2 | General Test Preparation for CUET

Algebra: Functions Questions - 2 | General Test Preparation for CUET

⇒ 570 + 45 + 10 625 

The question is "Find the value of [√1] + [√2] + [√3] +……………………………………………………+ [√100]?"

Hence the answer is "625"

Choice B is the correct answer.

Question 16: Find the value of x for which x[x] = 39? 

A. 6.244

B. 6.2

C. 6.3

D. 6.5

Answer. 6.5

Explanation.

When x = 7,
x[x] = 7 * 7 = 49
When x = 6,
x[x] = 6 * 6 = 36 
Therefore, x must lie in between 6 and 7 ⇒ [x] = 6

Algebra: Functions Questions - 2 | General Test Preparation for CUET 

The question is "Find the value of x for which x[x] = 39?"

Hence the answer is "6.5"

Choice D is the correct answer.

Question 17: Find the value of x for which x[x] = 15? 

A. 3.5

B. 5

C. 6.1

D. None of these

Answer. None of these

Explanation.

Using similar approach as previous question, [x] = 3 

x = 15/3 ⇒ x = 5 which is not possible since 3 < x < 4 

The question is "Find the value of x for which x[x] = 15?"

Hence the answer is "None of these"

Choice D is the correct answer.

Question 18: If f(x) = 1/g(x), then which of the following is correct? 

A. f(f(g(g(f(x))))) = g(f(g(g(g(x)))))

B. f(f(f(g(g(g(f(g(x)))))))) = g(g(g(g(f(g(f(f(x))))))))

C. f(f(g(f(x)))) = g(g(f(g(x))))

D. f(g(f(f(g(f(g(g(x)))))))) = g(g(g(g(f(f(f(f(x))))))))

Answer. f(g(f(f(g(f(g(g(x)))))))) = g(g(g(g(f(f(f(f(x))))))))

Explanation.

Given, f(x) = 1/g(x) ⇒ f(x).g(x) = 1 which implies that f(x) and g(x) are essentially inverse of one another.
So, one just has to look for an option which has equal number of fs and gs on both side of the equation. 

The question is "If f(x) = 1/g(x), then which of the given is correct?" 

Hence the answer is "f(g(f(f(g(f(g(g(x)))))))) = g(g(g(g(f(f(f(f(x))))))))"

Choice D is the correct answer.

Question 19: If f(x) = Algebra: Functions Questions - 2 | General Test Preparation for CUET Find the value of x for which f(x) = f-1(x)? 

A. -3

B. 2

C. Both A and B

D. None of these

Answer. Both A and B

Explanation.

f(x) = f-1(x) when f(x) = x 

Algebra: Functions Questions - 2 | General Test Preparation for CUET

 x + 6 = x2 + 2x
 x2 + x – 6 = 0
 (x+3) (x-2) = 0
 x = -3, 2 

The question is "Find the value of x for which f(x) = f-1(x)?"

Hence the answer is "Both A and B"

Choice C is the correct answer.

Question 20: If f(x) = |x| + |x+3| + |x+6| + ……………………………..+ |x+3t|, where x is an integer and t is a positive integer, find the minimum value of f(x) when t = 6? 

A. 63

B. 36

C. 30

D. 25

Answer. 36

Explanation.

When t = 3,
f(x) = |x| + |x+3| + |x+6| + ……………………………..+ |x+18|
Minimum value of this function will occur when x = -9 i.e. the middle term is at its minimum which is 0.
Therefore, f(-9) = 9 + 6 + 3 + 0 + 3 + 6 + 9
= 2 * 18
= 36

The question is "find the minimum value of f(x) when t = 6?"

Hence the answer is "36"

Choice B is the correct answer.

Question 21: In the previous question if t = 7, for how many values of x, f(x) will be minimum? 

A. 1

B. 2

C. 4

D. 8

Answer. 4

Explanation.

When t = 7,
f(x) = |x| + |x+3| + |x+6| + ……………………………..+ |x+21|
This expression has two middle terms: |x+9|, |x+12|
The value of f(x) will be minimized when the sum of the two middle terms are minimized
=) |x+9|+ |x+12| should be minimum
This happens when -12 ≤ x ≤ -9, Note that for x = -12, -11, -10, -9 the value of the sum of the middle terms = 3.
Therefore, for all 4 values of x, f(x) will have minimum value.

The question is "In the previous question if t = 7, for how many values of x, f(x) will be minimum?"

Hence the answer is "4"

Choice C is the correct answer.


Question 22If f(x2 – 1) = x4 – 7x2 + k1 and f(x3 – 2) = x6 – 9x3 + k2 then the value of (k2 – k1) is

A. 6

B. 7

C. 8

D. 9

E. None of the above
Answer. 8

Explanation. 
Given Data

f(x2 – 1) = x4 – 7x2 + k1

f(x3 – 2) = x6 – 9x3 + k2

Approach and Solution

When x2 = 1, f(x2 – 1) = f(1 - 1) = f(0) =(1)2 - 7(1) + k1 
f(0) = - 6 + k1 ..........(1)
Essentially, we have replaced all x2 with 1.

When x3 = 2,f(x3 – 2) = f(2 - 2) = f(0) =(2)2 - 9(2) + k2
f(0) = - 14 + k2 ..........(2)
Essentially, we have replaced all x3 with 2.

Equating f(0) in equations (1) and (2)
(-6 + k1) = (-14 + k2)
or k2 - k1 = 8

Question 23Which of the following is not an odd function?

(1) f(x) = -x3

(2) f(x) = x5

(3) f(x) = x2 – x

(4) f(x) = |x|3

Answer. f(x) = |x|3

Explanation. 

An odd function is a function whose value reverses in sign for a reversal in sign of its argument. i.e. f(x) = -f(-x).

Except f(x) = |x|3 all other functions mentioned in the choices change values.

The document Algebra: Functions Questions - 2 | General Test Preparation for CUET is a part of the CUET Course General Test Preparation for CUET.
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FAQs on Algebra: Functions Questions - 2 - General Test Preparation for CUET

1. What are functions in algebra?
Ans. In algebra, a function is a rule that assigns each element from one set, called the domain, to exactly one element from another set, called the range. These sets can have numbers, variables, or expressions as their elements.
2. How do you determine if a relation is a function?
Ans. To determine if a relation is a function, we need to check if each input value in the domain is associated with a unique output value in the range. If there is any input value that is associated with more than one output value, then the relation is not a function.
3. What is the difference between domain and range in a function?
Ans. The domain of a function is the set of all possible input values for which the function is defined. It represents the independent variable. On the other hand, the range of a function is the set of all possible output values that the function can produce. It represents the dependent variable.
4. How do you find the domain of a function?
Ans. To find the domain of a function, we need to identify any restrictions on the input values. Common restrictions include avoiding division by zero, avoiding square roots of negative numbers, and avoiding logarithms of non-positive numbers. Once these restrictions are identified, we can determine the set of all valid input values.
5. Can a function have the same output for different input values?
Ans. No, a function cannot have the same output for different input values. According to the definition of a function, each input value must be associated with a unique output value. If two different input values yield the same output, it violates the concept of a function.
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