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# Test: Graphs & Algebra Of Functions

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## 10 Questions MCQ Test Mathematics For JEE | Test: Graphs & Algebra Of Functions

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Test: Graphs & Algebra Of Functions - Question 1

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

Detailed Solution for Test: Graphs & Algebra Of Functions - Question 1

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.

Test: Graphs & Algebra Of Functions - Question 2

### Which of the following is incorrect?

Detailed Solution for Test: Graphs & Algebra Of Functions - Question 2

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.

Test: Graphs & Algebra Of Functions - Question 3

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

Detailed Solution for Test: Graphs & Algebra Of Functions - Question 3

f(x) = 3x + 1,  g(x) = x2 + 2
f-g = (3x+1) - (x2 + 2)
= 3x + 1 - x2 - 2
= 3x - x2 -1

Test: Graphs & Algebra Of Functions - Question 4

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

Detailed Solution for Test: Graphs & Algebra Of Functions - Question 4

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,x∈R

Test: Graphs & Algebra Of Functions - Question 5

f(x) = x is called______.

Detailed Solution for Test: Graphs & Algebra Of Functions - Question 5

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.

Test: Graphs & Algebra Of Functions - Question 6

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

Detailed Solution for Test: Graphs & Algebra Of Functions - Question 6

f(g(2)) compare f(gx) x=2
on comparing g(x)=x, g(2)=2
f(g(x)) = f(2) = x= 22= 4

Test: Graphs & Algebra Of Functions - Question 7

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

Detailed Solution for Test: Graphs & Algebra Of Functions - Question 7

Test: Graphs & Algebra Of Functions - Question 8

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:

Detailed Solution for Test: Graphs & Algebra Of Functions - Question 8

Let the no. of units sold be x.
Monthly pay: y = 200 + 5x

Test: Graphs & Algebra Of Functions - Question 9

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

Detailed Solution for Test: Graphs & Algebra Of Functions - Question 9

For the graph y=x2
The least value of x2 is zero and square of any number will also be zero.

Test: Graphs & Algebra Of Functions - Question 10

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

Detailed Solution for Test: Graphs & Algebra Of Functions - Question 10

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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