Question

What are the twelve basic functions?

Answer 1

Hint: The hint to proceed in this problem can be the names of these functions. Like which functions are generally there in the list of the basic functions. Those are identity functions. Square function, cubic function, absolute function etc. we will study the 12 one by one.

Complete step by step solution:
We know that function is an inseparable part of mathematics. We can define a function as a relationship between an independent variable and dependent variable. Generally we express the function as \[f\left( x \right)\] and we read it as f of x. so there are different functions in mathematics that will be noted below.

Function definition	Name of the Function	Explanation
1) Identity function	\[f\left( x \right) = x\]	In this a function is defined as whatever the value of the variable is the value of the function itself.
2) Square function	\[f\left( x \right) = {x^2}\]	This function is having the power of variable raised to 2. Generally we can say quadratic equations are the square functions.
3) Cubic function	\[f\left( x \right) = {x^3}\]	This function is having the power of variable raised to 3. We can say that cubic equations are the cubic functions.
4) Square root function	\[f\left( x \right) = \sqrt x \]	In this the value of the variable is written under the root. The value of the variable is high but the value of the function is not that high.
5) Reciprocal function	\[f\left( x \right) = \dfrac{1}{x}\]	This is the reciprocal function written in the form of a fixed numerator as 1 and the denominator is the variable.
6) Even function	\[f\left( x \right) = f\left( { - x} \right)\]	If a function is having only symmetry about the y axis, it is said to be an even function such that the value of that variable for negative is the existing value. But it won’t mean that an even powered function is always an even function.
7) Odd function:	\[f\left( x \right) = - f\left( { - x} \right)\]	If a function is having only symmetry about the origin, it is said to be an odd function such that the value of that variable for negative is the negative value of the function. But it won’t mean that an odd powered function is always an even function.
8) Natural logarithm function	\[f\left( x \right) = \ln x\]	This is a natural logarithm function.
9) Exponential function	\[f\left( x \right) = {e^x}\]	This is the exponential function raised to the power of the variable. Sometimes the power can be negative.These are the functions used in the rates equation.
10) Constant function	\[f\left( x \right) = C\]	This function has a constant value C for any value of x.
11) Sine function	\[f\left( x \right) = \sin x\]	This is the sinusoidal function. This is used in mathematics as well as physics. This is the waveform of the function.
12) Cos function	\[f\left( x \right) = \cos x\]	This is a cos function. This is also in the form of a wave.

So these are the basic functions in mathematics.

Note:
Apart from the functions above there are various functions in mathematics which are use frequently for expressing the functions. Note that functions are just a relation showed between the variable with the help of graph can also be expressed.