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Which of the following is not an example of polynomial function ?
A polynomial function is a function which involves only nonnegative 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(x_{1}) = f(x_{2}) for all x_{1},x_{2} ∈ 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.
If f and g are two functions over real numbers defined as f(x) = 3x + 1, g(x) = x^{2} + 2, then find fg
f(x) = 3x + 1, g(x) = x^{2} + 2
fg = (3x+1)  (x^{2} + 2)
= 3x + 1  x^{2}  2
= 3x  x^{2} 1
The function f : R → R defined by y = f(x) = 5 for each x ∈ R is
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(x_{1}) = f(x_{2}) for all x_{1},x_{2 }∈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.
If f(x) = x^{2} and g(x) = x are two functions from R to R then f(g(2)) is:
f(g(2)) compare f(gx) x=2
on comparing g(x)=x, g(2)=2
f(g(x)) = f(2) = x^{2 }= 2^{2}= 4
The graph of the function f : R → R defined by f(x) = x
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:
Let the no. of units sold be x.
Monthly pay: y = 200 + 5x
Which is not true for the graph of the real function y = x^{2}:
For the graph y=x^{2}
The least value of x^{2} is zero and square of any number will also be zero.
If f(x) = x^{2} and g(x) = cosx, which of the following is true?
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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