f(x+h) – f(x)h±0. Simplify your answer1Given f(x)=-x-2, find the difference quotient,hcompletely so that no factor of h remains in the denominator (However, terms within a factor in thedenominator can contain h).

Answered: Given f(x)=- , find the difference…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

f(x+h) – f(x)h±0. Simplify your answer
1
Given f(x)=-
x-2
, find the difference quotient,
h
completely so that no factor of h remains in the denominator (However, terms within a factor in the
denominator can contain h).

Expert Solution

Step 1

The function $f (x)$ is a rule that associates or fixes a number to the particular point x. If $y = f (x),$ then the independent variable x is called the input of the function and the dependent variable y is called the output of the function.

The general form of a polynomial function of degree n is given by $a_{0} x^{n} + a_{1} x^{n - 1} + \cdot \cdot \cdot + a_{n}$ , where $a_{0} \neq 0$ . The function in the form $f (x) = \frac{p (x)}{q (x)}$ , where $p (x)$ and $q (x)$ are the polynomial function is called a rational function.