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A change machine can accept $1, $5, $10, and $20 bills and returns quarters. What is the domain and range of this situation?

Svet_ta [14]

Answer:

Domain {1,5,10,20}

Ranger {4,20,40,80}

Step-by-step explanation:

$1=4 quarters

$5=20 quarters

$10=40 quarters

$20=80 quarters

Domain {1,5,10,20}

Ranger {4,20,40,80}

5 0

3 years ago

Danika concludes that the following functions are inverses of each other because f(g(x)) = x. Do you agree with Danika? Explain

arsen [322]

We cannot agree with Danika. Why? Well, The reasoning is given as follows:

Two functions are inverses of each other if and only if it is true that the composition function is given by:

$f(g(x))=x$

Everything is ok up to this point, right?. But let's prove that this is not fulfilled for these functions, then:

$f(x)=\left | x \right | \\ \\ g(x)=-x \\ \\ f(g(x))=\left| -x \right |=\left | -1 \right | \left | x \right |=\left | x \right | \\ \\ \therefore f(g(x))=\left | x \right | \neq x$

As you can see we did not obtain the function that matches the definition of inverse functions. For that reason we can't agree with Danika.

5 0

3 years ago

Read 2 more answers

What is an equation of the line that passes through the points (6,2) and

S_A_V [24]

$(\stackrel{x_1}{6}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{6}}}\implies \cfrac{-1}{1}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{-1}(x-\stackrel{x_1}{6}) \\\\\\ y-2=-x+6\implies y=-x+8$