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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, Domain: R; Range: R

In option C, range of constant function is a single value.

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:

QUESTION: 4

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

Solution:

Since the value of y remains fixed i.e. y=5 for any value of input x. Therefore, f is a constant function.

QUESTION: 5

f(x) = x is called

Solution:

In mathematics, 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. In equations, the function is given by f(x) = x.

QUESTION: 6

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

Solution:

In any composite function f(g(x)), the output of the first function i.e. g(x) becomes the input of the second function f(x).

Here, the output of g(x) i.e. g(2)= 2. Therefore, this output will become the input of the function f(x) and yield f(g(2))= x^{2}= 2^{2}= 4

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:

Reason: The minimum value of x^{2}= 0.

Since the square of any real number can’t be negative, it is either equal to or greater than zero.

QUESTION: 10

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

Solution:

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