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QUESTION: 1

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

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

Which of the following is incorrect?

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

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

Solution:

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

f-g = (3x+1) - (x^{2} + 2)

= 3x + 1 - x^{2} - 2

= 3x - x^{2} -1

QUESTION: 4

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

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

f(x) = x is called

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

If f(x) = x^{2} and g(x) = x are two functions from R to R then f(g(2)) is

Solution:

As f(g(x)) = f(x)g(x),

so, f(g(2)) = f(2) g(2)

= (2)^{2 }* 2

= 4 * 2

= 8

QUESTION: 7

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

Solution:

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

Solution:

Let the no. of units sold be x.

Monthly pay: y = 200 + 5x

QUESTION: 9

Which is not true for the graph of the real function y = x^{2}:

Solution:

For the graph y=x^{2}

The least value of x^{2} is zero and square of any number will also be zero.

QUESTION: 10

If f(x) = x^{2} and g(x) = cosx, which of the following is true?

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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