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Sphinxa [80]
3 years ago
7

Determine whether each pair of functions are inverse functions. Write yes or no.

Mathematics
1 answer:
Tatiana [17]3 years ago
6 0

Answer: No

Step-by-step explanation:

There are two ways to solve this. The first way is to calculate g(f(x)) (or f(g(x))). If f and g are inverse functions f(g(x)) = g(f(x)) = x.

g(f(x)) = (1/4)(2sqrt(x - 5))^2 - 5

= (1/4)*2^2*sqrt(x - 5)^2 - 5

= (1/4)*4*(x - 5) - 5

= x - 5 - 5

= x - 10

g(f(x)) = x - 10 =/= x, so the two functions are not inverse functions.

You can also solve this by using a test value a and calculating g(f(a)). If f and g are inverse functions, the result will be a.

For example, let a = 6.

f(6) = 2*sqrt(6 - 5)

= 2*sqrt(1)

= 2*1

= 1

g(f(6)) = g(1)

= (1/4)*1^2 - 5

= (1/4)*1 - 5

= 1/4 - 5

= -4 3/4

=/= 6

Therefore f and g are not inverse functions

Please note that this technique does not work in the other direction. If g(f(a)) = a, this does NOT prove that f and g are inverse functions.

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The sum of two consecutive mile markers on the interstate is 417417. Find the numbers on the markers
noname [10]

Hello from MrBillDoesMath!

Answer:

The first marker is labeled 208708; the second (consecutive) one 208709                  


Discussion:

Call the first mile marker "m". Then

m + (m+1) = 417417            => combine like terms

2m + 1 = 417417                 => subtract 1 from both sides

2m =  417416                     => divide both sides by 2

m  = 417416/2  = 208708                  

Note: m and (m+1) are consecutive as they immediately follow each other in the set of integers.

Thank you,

MrB

5 0
3 years ago
Find tan A for the triangle below.<br><br> a 1.5<br> b. 0.667<br> C. 0.832<br> d. 1.202
Kaylis [27]

Answer:

B

Step-by-step explanation:

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3 0
2 years ago
About your photograph 4 in wide and 6in long the photograph is enlarged and their larger is proportional to the original photogr
Bad White [126]
18 inches.

12/4=3 so you would multiply 6•3 to get 18
4 0
3 years ago
Read 2 more answers
Which equation has the solutions x = -3 ± √3i/2 ?
Maurinko [17]

Answer:Answer is option C : [x^{2} + 3x + 3 ] =0

Note:  None of options matches with given question.

instead of "-3" , there should be "-\frac{3}{2}".

Step-by-step explanation:

Note:  None of options matches with given question.

instead of "-3" , there should be "\frac{3}{2}".  

Here, First thing you have to observe the nature of roots.

∴ x = -\frac{3}{2}+\frac{\sqrt{3}}{2}i and x = -\frac{3}{2}-\frac{\sqrt{3}}{2}

∴ [ x+(\frac{3}{2}-\frac{\sqrt{3}}{2}i) ][ x+(\frac{3}{2}+\frac{\sqrt{3}}{2}i) ]=0

∴ [ x^{2} + x(\frac{3}{2}+\frac{\sqrt{3}}{2}i)+ x(\frac{3}{2}-\frac{\sqrt{3}}{2}i) + (\frac{3}{2}-\frac{\sqrt{3}}{2}i)(\frac{3}{2}+\frac{\sqrt{3}}{2}i) ]=0

∴ [x^{2} + \frac{3}{2}x + \frac{\sqrt{3}}{2}ix + \frac{3}{2}x - \frac{\sqrt{3}}{2}ix + (3-\frac{\sqrt{3}}{2}i)(3+\frac{\sqrt{3}}{2}i) ] =0

∴ [x^{2} + 3x + (\frac{3}{2}-\frac{\sqrt{3}}{2}i)(\frac{3}{2}+\frac{\sqrt{3}}{2}i) ] =0

∴ [x^{2} + 3x + \frac{9}{4} - (\frac{\sqrt{3}}{2}i)(\frac{\sqrt{3}}{2}i) ] =0

∴ [x^{2} + 3x + \frac{9}{4} - (\frac{3}{4}) i^{2} ] =0

∴ [x^{2} + 3x + \frac{9}{4} + (\frac{3}{4}) ] =0

∴ [x^{2} + 3x + \frac{12}{4} ] =0  

∴ [x^{2} + 3x + 3 ] =0  

Thus, Answer is option C : <em>[x^{2} + 3x + 3 ] =0  </em>

6 0
3 years ago
How do you us the distributive property to work out (4+5)6
777dan777 [17]
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Hope this helps!

7 0
3 years ago
Read 2 more answers
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