Test: Graphs And Algebra Of Functions

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.

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

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

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

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.

As fg(x)= f(x)g(x), 
so, (fg)(2) = f(2)g(2)
= (2)^2 * 2
= 4*2   
=8

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

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

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