Chapter 2: Q19. (page 66)

State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.
$19 . g (x) = 10 + \frac{2}{x^{2}}$

Short Answer

Expert verified

No, the function $g (x) = 10 + \frac{2}{x^{2}}$ is not a linear function.

Step by step solution

– Definition of a linear equation and linear function.

In a linear equation the exponent of each variable is 1 and the variables may not be multiplied together. The graph of a linear equation is always a line.

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 function is:

$g (x) = 10 + \frac{2}{x^{2}}$

This function can be rewritten as:

$g (x) = 10 + 2 x^{- 2}$ $[∵ a^{- n} = \frac{1}{a^{n}}]$

– Check whether the equation is linear or not.

In the function $g (x) = 10 + 2 x^{- 2}$ the exponent of x is -2.

So, the function $g (x) = 10 + \frac{2}{x^{2}}$ is not a linear function because x has an exponent other than 1.

Thus,the required answer is “No” because the function $g (x) = 10 + \frac{2}{x^{2}}$ is not a linear function.

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State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.
$19 . g (x) = 10 + \frac{2}{x^{2}}$

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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State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.19.g(x)=10+2x2

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

Logic and Functions

Statistics

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Study anywhere. Anytime. Across all devices.

State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.
$19 . g (x) = 10 + \frac{2}{x^{2}}$