Here you will learn what is square function with definition, graph, domain and range. Let’s begin – Square Function The function that associates a real number x to its square i.e. \(x^2\) is called square function. Since \(x^2\) is defined for all x \(\in\) R. So, we defined the square function as follows : Definition …
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Here you will learn what is square root function with definition, graph, domain and range. Let’s begin – Square Root Function The function that associates a real number x to +\(\sqrt{x}\) is called square root function. Since \(\sqrt{x}\) is real for x \(ge\) 0. So, we defined the square root function as follows : Definition …
Here you will learn what is reciprocal function with definition, graph and domain and range. Let’s begin – Reciprocal Function The function that associates a real number x to its reciprocal \(1\over x\) is called the reciprocal function. Since \(1\over x\) is not defined for x = 0. So, we define reciprocal function as follows …
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Here you will learn what is logarithmic function graph, formula, domain and range. Let’s begin – Logarithmic Function Definition : If a > 0 and a \(\ne\) 1, then the function defined by f(x) = \(log_a x\), x > 0 is called the logarithmic function. We know that logarithmic function and the exponential function are …
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Here you will learn what is exponential function graph, formula, domain and range. Let’s begin – Exponential Function Formula Definition : If a is a positive real number other than unity, then a function that associates each x \(\in\) R to \(a^x\) is called the exponential function. In other words, a function f : R …
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Here you will learn what is signum function definition, graph, domain and range. Let’s begin – What is Signum Function ? Definition : The function f defined by f(x) = \(\begin{cases} | x |\over x, & \text{if}\ |x| \ne 0 \\ 0, & \text{if}\ x = 0 \end{cases}\) or, f(x) = \(\begin{cases} 1, & \text{if}\ …
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Here you will learn definition, graph, domain and range of fractional part function. Let’s begin – Fractional Part Function Definition : For any real number x, we use the symbol {x} to denote fractional part or decimal part of x. For example, {3.45} = 0.45, {-2.75} = 0.25, {-0.55} = 0.45, {3} = 0, {-7} …
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Here you will learn what is smallest integer function definition, graph and its domain and range with examples. Let’s begin – Smallest Integer Function (Ceiling Function) Definition : For any real number x, we use the symbol \(\lceil x \rceil\) to denote the smallest integer greater than or equal to x. For example, \(\lceil 4.7 …
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Here you will learn what is identity function with definition, graph and examples. Let’s begin – What is Identity Function ? Definition : The function that associates each real number to itself is called the identity function. It is usually denoted by I. Thus, the function I : R \(\rightarrow\) defined by I(x) = x …
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Here you will learn what is constant function with definition, graph and examples. Let’s begin – What is Constant Function ? Definition : If k is a fixed real number, then a function f(x) given by f(x) = k for all x \(\in\) R is called a constant function. For Example, f(x) = 2 , …
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