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Chapter 1: Problem 45

Find the value(s) of \(x\) for which \(f(x)=g(x)\). $$f(x)=x^{2}, \quad g(x)=x+2$$

Short Answer

Expert verified
The values of \(x\) for which \(f(x)=g(x)\) are \(x=2\) and \(x=-1\).

Step by step solution

01

Equate the two functions

First, set the two functions equal to each other.\[f(x) = g(x)\]Or, \[x^{2} = x + 2\]
02

Rearrange terms to form a quadratic equation

Subtract \(x\) and 2 from both sides of the equation to set it to zero and form a standard quadratic equation. \[x^{2} - x - 2 = 0\]
03

Factor the quadratic equation

Next, factor the quadratic equation into two binomial factors. \[(x-2)(x+1) = 0\]
04

Set each factor equal to zero and solve for \(x\)

This will give the values of \(x\) that satisfy the equation. \[x-2 = 0 \Rightarrow x=2\] and then \[x+1 = 0 \Rightarrow x=-1\]

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Most popular questions from this chapter

Sketch the graph of the function. $$f(x)=\left\\{\begin{array}{ll}1-(x-1)^{2}, & x \leq 2 \\\\\sqrt{x-2}, & x>2\end{array}\right.$$

Sketch the graph of the function. $$k(x)=\left\\{\begin{array}{ll}2 x+1, & x \leq-1 \\\2 x^{2}-1, & -11\end{array}\right.$$

The percents \(p\) of prescriptions filled with generic drugs in the United States from 2004 through 2010 (see figure) can be approximated by the model \(p(t)=\left\\{\begin{array}{ll}4.57 t+27.3, & 4 \leq t \leq 7 \\ 3.35 t+37.6, & 8 \leq t \leq 10\end{array}\right.\) where \(t\) represents the year, with \(t=4\) corresponding to \(2004 .\) Use this model to find the percent of prescriptions filled with generic drugs in each year from 2004 through \(2010 .\) (Source: National Association of Chain Drug Stores) (GRAPH CAN'T COPY)

Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$f(x)=x^{3}-1$$

Find the difference quotient and simplify your Answer: $$f(x)=x^{2 / 3}+1, \quad \frac{f(x)-f(8)}{x-8}, \quad x \neq 8$$
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