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gulaghasi [49]
3 years ago
13

If f(x) = x + 7 and g(x) = 1 / x - 13, whaf is the domain of (f°g)(x)?​

Mathematics
1 answer:
ZanzabumX [31]3 years ago
6 0

Answer: Choice D) x can be anything but 13

========================================================

Explanation:

The domain of (f \circ g)(x) = f(g(x)) is the same as the domain of g(x)

The domain for g(x) is \{x|x \ne 13\} saying we can plug in any number we want as long as it's not 13. This is to avoid dividing by zero. The same domain applies for the composite function because

f(x) = x+7\\\\\\f(g(x)) = g(x)+7\\\\\\f(g(x)) = \frac{1}{x-13}+7\\\\\\(f \circ g)(x) = \frac{1}{x-13}+7\\\\\\

and we can see that we still need to kick out x = 13 from the domain to avoid the division by zero issue.

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The neighborhood swimming pool is 14 feet long, 11 feet wide, and 3 feet deep. Which formula below should be used to find how mu
My name is Ann [436]

Answer:

  D.  14 feet × 11 feet × 3 feet

Step-by-step explanation:

The volume of a rectangular prism is the product of its dimensions:

  V = LWH

  V = (14 ft)(11 ft)(3 ft) . . . . . matches choice D

4 0
2 years ago
Using the Principle of Mathematical Induction, prove that . n ^2 − n is even for n ≥ 1​
Tamiku [17]

Base case: if <em>n</em> = 1, then

1² - 1 = 0

which is even.

Induction hypothesis: assume the statement is true for <em>n</em> = <em>k</em>, namely that <em>k</em> ² - <em>k</em> is even. This means that <em>k</em> ² - <em>k</em> = 2<em>m</em> for some integer <em>m</em>.

Induction step: show that the assumption implies (<em>k</em> + 1)² - (<em>k</em> + 1) is also even. We have

(<em>k</em> + 1)² - (<em>k</em> + 1) = <em>k</em> ² + 2<em>k</em> + 1 - <em>k</em> - 1

… = (<em>k</em> ² - <em>k</em>) + 2<em>k</em>

… = 2<em>m</em> + 2<em>k</em>

… = 2 (<em>m</em> + <em>k</em>)

which is clearly even. QED

8 0
3 years ago
A standard coffee mug has a capacity of 16 fluid ounces. If Annie needs to fill 26 mugs with coffee, how many total quarts of co
r-ruslan [8.4K]
First let's find how many total ounces it would be by multiplying 16 ounces by the number of mugs (26).

16 × 26 = 416

So she needs 416 ounces of coffee. Now we have to convert ounces to quarts. We need to know that there are 32 ounces per quart. So to find quarts we divide 416 ounces by 32...

416 ÷ 32 = 13 quarts

*FYI- since the mugs hold 16 ounces we can see that 16 is half of 32 so we could have just taken 1/2 of 26 mugs which is 13.
4 0
3 years ago
Add the following decimals​
Fantom [35]

Answer:

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Step-by-step explanation:

hope it helps<333

5 0
3 years ago
Find the values of x and y for which the lines are parallel.
bearhunter [10]
The answer:  " x = 68, y = 72 " .
____________________________
Explanation:
________________________________________
46 + (x - 3) + (y - 3) = 180 .

46 + 1(x - 3) + 1(y-3) = 180 .

46 + 1x - 3 + 1y - 3 = 180 .

46 - 3 - 3 + 1x + 1y = 180 .

40 + x + y = 180 ;

Subtract "40" from EACH SIDE of the equation:
______________________________________
 40 + x + y - 40 = 180 - 40 ;

 to get:

x + y = 140 ;
_____________________________________
Now:
_____________________________________
65 = (x - 3) ;


↔  x - 3 = 65 ;

Add "3" to EACH SIDE of the equation;

    x - 3 + 3 = 65 + 3 ;

to get:
 
           x = 68 .
______________________________
Now:

Since:  "x + y = 140" ;

Let us plug in our known value, "68" ;  for "x" ;

to solve for "y" ;
__________________________________
   x + y = 140 ;
 
  68 + y = 140 ;

↔ y + 68 = 140 ;

Subtract "68" from EACH SIDE of the equation; to isolate "y" on one side of the equation; and to solve for "y" ;
______________________________________________
   y + 68 - 68 = 140 = 68 ;

                  y = 72 .
______________________________________________
So,  solve for "x" and "y".

x = 68, y = 72 .
_______________________________________________
5 0
3 years ago
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