Test: Graphs & 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.

f(g(2)) compare f(gx) x=2
on comparing g(x)=x, g(2)=2
f(g(x)) = f(2) = x² = 2²= 4

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