Sets, Relations and Functions Test

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Sets, Relations and Functions Test - 4

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Weekly Quiz Competition

Question 1
2 / -0.83

Which of the following is not an example of polynomial function ?

A
g(x) = 8x² + 5x –2

B
p(x) = 5x³ + 3x² + x –2

C
h(x) = (∛x - 1)/x

D
f(x) = 3x² + x –2

Solution

A polynomial function is a function which involves only non-negative integer powers or only positive integer exponents of a variable in an equation.
In option C, powers of x are negative and fractional.
Question 2
2 / -0.83

Which of the following is incorrect?

A
Modulus function, Domain: R; Range: [0, infinity)

B
Signum function, Domain: R; Range: {-1, 0,1}

C
Constant function, Domain: R; Range: R

D
Identity function, Domain: R; Range: R

Solution

Constant Function is defined as the real valued function.
f : R →R, y = f(x) = c for each x ∈R and c is a constant.
So, this function basically associate each real number to a constant value.
It is a linear function where f(x₁ ) = f(x₂ ) for all x₁ ,x₂ ∈R
For f : R →R, y = f(x) = c for each x ∈R
Domain = R
Range = {c}
The value of c can be any real number.
Question 3
2 / -0.83

If f and g are two functions over real numbers defined as f(x) = 3x + 1, g(x) = x² + 2, then find f-g

A
x² +1

B
3x + x²

C
3x –x² -1

D
x² +1-3x

Solution

f(x) = 3x + 1, g(x) = x² + 2
f-g = (3x+1) - (x² + 2)
= 3x + 1 - x² - 2
= 3x - x² -1
Question 4
2 / -0.83

The function f : R →R defined by y = f(x) = 5 for each x ∈R is

A
Modulus function

B
Signum function

C
Identity function

D
Constant function

Solution

Constant Function is defined as the real valued function.
f: R →R, y = f(x) = c for each x ∈R and c is a constant.
So ,this function basically associate each real number to a constant value.
It is a linear function where f(x₁ ) = f(x₂ ) for all x₁ ,x₂ ∈R
Question 5
2 / -0.83

f(x) = x is called______.

A
An identity function

B
A constant function

C
Inverse function

D
Step function

Solution

An identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument. That is, for f being identity, the equality f(x) = x holds for all x.
Question 6
2 / -0.83

If f(x) = x² and g(x) = x are two functions from R to R then f(g(2)) is:

A
8

B
4

C
1

D
2

Solution

f(g(2)) compare f(gx) x=2
on comparing g(x)=x, g(2)=2
f(g(x)) = f(2) = x² = 2² = 4
Question 7
2 / -0.83

The graph of the function f : R →R defined by f(x) = |x|

A
A line lying in first and third quadrant

B
A straight line

C
Symmetrical with respect to y –axis

D
A pair of parallel lines

Solution
Question 8
2 / -0.83

If monthly pay of salesman is 'y 'and includes basic pay $200 plus a commission of $5 for every unit he sales then function for this can be written as:

A
x = 205 + 5y

B
200 + 5xy

C
x = 387 + 5y

D
y = 200 + 5x

Solution

Let the no. of units sold be x.
Monthly pay: y = 200 + 5x
Question 9
2 / -0.83

Which is not true for the graph of the real function y = x² :

A
The least value of x² is one and will be so when x = 1.

B
For this function domain = Real numbers

C
The parabola will open upward.

D
The graph of the given function is a parabola.

Solution

For the graph y=x²
The least value of x² is zero and square of any number will also be zero.
Question 10
2 / -0.83

If f(x) = x² and g(x) = cosx, which of the following is true?

A
f + g is even function

B
f –g is an odd function

C
f + g is not defined

D
f + g is an odd function

Solution

if f(x) is an odd function
So, f(−x)=−f(x)
F(−x)=cos(f(−x))
=cos(−f(x))
=cos(f(x))
=F(x)
So cos(f(x)) is an even function
So, f(x) and g(x) is an even function

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Sets, Relations and Functions Test - 4

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Question 1

g(x) = 8x2 + 5x –2

p(x) = 5x3 + 3x2 + x –2

h(x) = (∛x - 1)/x

f(x) = 3x2 + x –2

Solution

Question 2

Modulus function, Domain: R; Range: [0, infinity)

Signum function, Domain: R; Range: {-1, 0,1}

Constant function, Domain: R; Range: R

Identity function, Domain: R; Range: R

Solution

Question 3

x2 +1

3x + x2

3x –x2 -1

x2 +1-3x

Solution

Question 4

Modulus function

Signum function

Identity function

Constant function

Solution

Question 5

An identity function

A constant function

Inverse function

Step function

Solution

Question 6

8

4

1

2

Solution

Question 7

A line lying in first and third quadrant

A straight line

Symmetrical with respect to y –axis

A pair of parallel lines

Solution

Question 8

x = 205 + 5y

200 + 5xy

x = 387 + 5y

y = 200 + 5x

Solution

Question 9

The least value of x2 is one and will be so when x = 1.

For this function domain = Real numbers

The parabola will open upward.

The graph of the given function is a parabola.

Solution

Question 10

f + g is even function

f –g is an odd function

f + g is not defined

f + g is an odd function

Solution

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g(x) = 8x² + 5x –2

p(x) = 5x³ + 3x² + x –2

f(x) = 3x² + x –2

x² +1

3x + x²

3x –x² -1

x² +1-3x

The least value of x² is one and will be so when x = 1.