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4 years ago

Given the function a(x)=4x−8 with range R: {0,4,8}, which of the following represents the domain, D of function a?

Mathematics

2 answers:

hram777 [196]4 years ago

8 0

the correct option is D

4(2)-8= 0

4(3)-8 = 4

4(4)-8 = 8

cricket20 [7]4 years ago

5 0

Answer:

Option D.

Step-by-step explanation:

The given function is

$a(x)=4x-8$

We need to find the domain of the function for range R:{0,4,8}.

Domain is the set of input values and range is the set of output values.

Substitute a(x)=0 in the given function.

$0=4x-8$

$-4x=-8$

$x=2$

Substitute a(x)=4 in the given function.

$4=4x-8$

$12=4x$

$3=x$

Substitute a(x)=8 in the given function.

$8=4x-8$

$16=4x$

$4=x$

The input values of function for outputs 0, 4 and 8 are 2, 3 and 4 respectively.

Domain = {2,3,4}

Therefore, the correct option is D.

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3 years ago

(1 point) consider the function f(t)=⎧⎩⎨⎪⎪⎪⎪0,−5,−6,6,t<00≤t<11≤t<7t≥7;f(t)={0,t<0−5,0≤t<1−6,1≤t<76,t≥7; 1. wr

sergij07 [2.7K]

$f(t)=\begin{cases}0&\text{for }t$

Recall that

$u(t)=\begin{cases}0&\text{for }t$

Take it one piece at a time. For $t\ge0$ , we can scale $u(t)$ by -5:

$-5u(t)=\begin{cases}0&\text{for }t$

If we shift the argument by 1 and scale by -5, we have

$-5u(t-1)=\begin{cases}0&\text{for }t$

so if we subtract this from $-5u(t)$ , we'll end up with

$-5u(t)+5u(t-1)=\begin{cases}0&\text{for }t$

For the next piece, we can add another scaled and shifted step like

$-6u(t-1)+6u(t-7)=\begin{cases}0&\text{for }t$

so that

$-5u(t)+5u(t-1)-6u(t-1)+6u(t-7)=\begin{cases}0&\text{for }t$

For the last piece, we add one more term:

$6u(t-7)=\begin{cases}0&\text{for }t$

and so putting everything together, we get $f(t)$ :

$f(t)\equiv-5u(t)+5u(t-1)-6u(t-1)+6u(t-7)+6u(t-7)$
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3 years ago