Chapter 2: Q24. (page 66)

Which of the functions $f (x) = 2 x + 4, g (x) = 7$ and $h (x) = x^{3} - x^{2} + 3 x$ is not linear.

Short Answer

Expert verified

The function $h (x) = x^{3} - x^{2} + 3 x$ is not a linear function.

Step by step solution

– Definition of a linear equation and linear function.

In a linear function, each input value has a unique output value. In other words, for each point in domain, there is a unique value in the range of function. It can be written as $f (x) = m x + b$ , where m and b are real numbers.

– Given information.

The given functions are:

$\begin{matrix} f (x) = 2 x + 4 \\ g (x) = 7 \\ h (x) = x^{3} - x^{2} + 3 x \end{matrix}$

– Check whether the equation is linear or not.

The given function $f (x) = 2 x + 4$ is in the form of $f (x) = m x + b$ , where both m=2 and b=4 are real values. So, the function $f (x) = 2 x + 4$ is a linear function.

The given function $g (x) = 7$ is a constant function and a constant function is always a linear function. So, the function $g (x) = 7$ is a linear function.

The given function $h (x) = x^{3} - x^{2} + 3 x$ is not a linear function because the exponent of $x$ is other than 1.

Thus, the function $h (x) = x^{3} - x^{2} + 3 x$ is not a linear function.

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Which of the functions $f (x) = 2 x + 4, g (x) = 7$ and $h (x) = x^{3} - x^{2} + 3 x$ is not linear.

Short Answer

Step by step solution

– Definition of a linear equation and linear function.

– Given information.

– Check whether the equation is linear or not.

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Which of the functions fx=2x+4,gx=7and hx=x3-x2+3xis not linear.

Short Answer

Step by step solution

– Definition of a linear equation and linear function.

– Given information.

– Check whether the equation is linear or not.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Pure Maths

Decision Maths

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

Which of the functions $f (x) = 2 x + 4, g (x) = 7$ and $h (x) = x^{3} - x^{2} + 3 x$ is not linear.