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MrRa [10]
2 years ago
7

Find the Value of k that will make the function f(x) continuous everywhere.​

Mathematics
1 answer:
cricket20 [7]2 years ago
6 0

well, if that function f(x) were to be continuos on all subfunctions, that means that whatever value 7x + k has when x = 2, meets or matches the value that kx² - 6 has when x = 2 as well, so then 7x + k = kx² - 6 when f(2)

f(x)= \begin{cases} 7x+k,&x\leqslant 2\\ kx^2-6&x > 2 \end{cases}\qquad \qquad f(2)= \begin{cases} 7(2)+k,&x\leqslant 2\\ k(2)^2-6&x > 2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 7(2)+k~~ = ~~k(2)^2-6\implies 14+k~~ = ~~4k-6 \\\\\\ 14~~ = ~~3k-6\implies 20~~ = ~~3k\implies \cfrac{20}{3}=k

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Step by step explanation:
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Minchanka [31]
Lets do this:-

A. 7 Sandwiches

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7 × $7.75 =  $54.25
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A is not d answer cuz d total of d lunches came to $113.50. 

B. 8 sandwiches

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8 × $7.75 =  $62
8 sandwiches cost $62.

10 × $4.50 = 45
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B is not d answer cuz d total of d lunches came to $113.50. 

C. 9 Sandwiches.

18 - 9 =  9

9 × $7.75 = 69.75
9 sandwiches cost $69.

9 × $4.50 = 40.50
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69 + 40.50 = 109.5

C is not d answer cuz d total of d lunches came to $113.50. 

D. 10 Sandwiches

18 - 10 = 8

10 × $7.75 = $77.75
10 sandwiches cost $77.75.

8 × $4.50 = $36
8 soups costs $36.

77.75 + 36 = <span>113.75

</span>D is not d answer cuz d total of d lunches came to $113.50. 

So, based on your answer choices there is no correct choice. <span />
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Answer:

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Step-by-step explanation:

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