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Consider functions fand gUsing a table of values, what is the approximate solution to the equation f(I) = g(I| to the nearest quarter of a unit?

Consider functions fand gUsing a table of values, what is the approximate solution-example-1
User Kissi
by
8.7k points

2 Answers

3 votes

The correct option is c.

The approximate solution to the equation
$f(x) = g(x)$ to the nearest quarter of a unit is
$x \approx 0.75$

To approximate the solution to the equation
$f(x) = g(x)$ to the nearest quarter of a unit using a table of values, we'll first calculate the values of
$f(x)$ and
$g(x)$ for a few different values of
$x$ and then find the value of
$x$ for which these two functions are closest to each other. Here are the steps:

1. Calculate the values of
$f(x)$ and
$g(x)$ for some values of
$x$.

We'll choose a range of values for
$x$ and calculate both
$f(x)$ and
$g(x)$:

For
$x = -2.25$:


$f(-2.25)=(-2.25-1)/((-2.25)^2+(-2.25)-1) \approx 0.683 g(-2.25)=3^2-2=7$

For
$x = -1.75$:


$f(-1.75)=(-1.75-1)/((-1.75)^2+(-1.75)-1) \approx-0.276 g(-1.75)=3^2-2=7$

For
$x = 0.50$:


$f(0.50)=(0.50-1)/((0.50)^2+(0.50)-1) \approx 0.732 g(0.50)=3^2-2=7$

For
$x = 0.75$:


$f(0.75)=(0.75-1)/((0.75)^2+(0.75)-1) \approx 0.889 g(0.75)=3^2-2=7$

2. Compare the values of
$f(x)$ and
$g(x)$ to find the closest match.

From the calculations above, we can see that the values of
$f(x)$ and
$g(x)$ are closest for
$x = 0.75$.

So, The answer is x=0.75.

User Josetta
by
8.0k points
4 votes

Given:

Two functions f(x) and g(x) are given.


\begin{gathered} f(x)=(x-1)/(x^2+x-1) \\ g(x)=3^x-2 \end{gathered}

Required:

Find the approximate solution to the equation f(x)=g(x) to the nearest quarter of the unit.

Step-by-step explanation:

(a) substitute x= 0.50in f(x) and g(x).


\begin{gathered} f(x)=(0.5-1)/((0.5)^2+0.5-1) \\ f(x)=(-0.5)/(-0.25) \\ f(x)=2 \end{gathered}
\begin{gathered} g(x)=3^(0.5)-2 \\ g(x)=-0.268 \end{gathered}

(b) substitute x=-1.75 in f(x) and g(x).


\begin{gathered} f(x)=(-1.75-1)/((-1.75)^2-1.75-1) \\ f(x)=(-2.75)/(0.38125) \\ f(x)=-7.2 \end{gathered}
\begin{gathered} g(x)=3^(-1.75)-2 \\ g(x)=-1.854 \end{gathered}

(c) substitute x= 0.75 in f(x) and g(x).


\begin{gathered} f(x)=(0.75-1)/((0.75)^2+0.75-1) \\ f(x)=(-0.25)/(0.3125) \\ f(x)=-0.8 \end{gathered}
\begin{gathered} g(x)=3^(0.75)-2 \\ g(x)=2.795 \end{gathered}

(d) substitute x= -2.25 in f(x) and g(x).


\begin{gathered} f(x)=(-2.25-1)/((-2.25)^2-2.25-1) \\ f(x)=(-3.25)/(1.8125) \\ f(x)=-1.793 \end{gathered}
\begin{gathered} g(x)=3^(-2.25)-2 \\ g(x)=-1.916 \end{gathered}

we can observe that at x = -2.25 the functions f(x) and g(x) has the approximate values.

Final Answ

User Chamara Paul
by
7.8k points
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