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Find the domain and range of the function f(x) = 2(2 - 3x).

 May 2, 2024

Best Answer 

 #1
avatar+202 
+1

So first off, let's write the function in standard form . Warning, this problem is quite straightforward, and you could probably geuss it...maybe

 

Distributing the 2 into the funcction gets us \(f(x) = -6x+4\)

 

DOMAIN

 

For the domain of this function, we just need to check whether or not there are any limits to what x can be. 

For example, in the function \(f(x) = \sqrt{2x+54}\), we must have the descriminant as greater or equal to 0, meaning there are restraints on the domain. 

 

In this function however, there are none, since x could be anything and it would not violate any concepts. 

 

Domain: All Real Numbers

 

RANGE:

Now, the range is limited usually because the domain is limited in someway. 

In this case, there are no limited to the domain, so there are no limits to the range. 

 

Range: All Real Numbers

 

Yep, both the range and domain are ALL REAL NUMBERS. 

 

In scientific notation:

 

Domain: \((-\infty, \infty)\)

Range: \((-\infty, \infty)\)

 

Thanks!

 May 2, 2024
 #1
avatar+202 
+1
Best Answer

So first off, let's write the function in standard form . Warning, this problem is quite straightforward, and you could probably geuss it...maybe

 

Distributing the 2 into the funcction gets us \(f(x) = -6x+4\)

 

DOMAIN

 

For the domain of this function, we just need to check whether or not there are any limits to what x can be. 

For example, in the function \(f(x) = \sqrt{2x+54}\), we must have the descriminant as greater or equal to 0, meaning there are restraints on the domain. 

 

In this function however, there are none, since x could be anything and it would not violate any concepts. 

 

Domain: All Real Numbers

 

RANGE:

Now, the range is limited usually because the domain is limited in someway. 

In this case, there are no limited to the domain, so there are no limits to the range. 

 

Range: All Real Numbers

 

Yep, both the range and domain are ALL REAL NUMBERS. 

 

In scientific notation:

 

Domain: \((-\infty, \infty)\)

Range: \((-\infty, \infty)\)

 

Thanks!

NotThatSmart May 2, 2024

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