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KatRina [158]
3 years ago
12

For which pair of function is (g*f)(a)=|a|-2

Mathematics
2 answers:
asambeis [7]3 years ago
7 0

Answer:

The correct pair is 3

Step-by-step explanation:

1.

f(a)=a^{2}-4 , g(a)=\sqrt{a} \\gof(a)=g(a^{2} -4)\\=\sqrt{a^{2}-4 } \neq |a|-2

2.

f(a)=\frac{1}{2\cdot a-1}, g(a)=2\cdot a -2\\gof(a)=g(\frac{1}{2\cdot a-1} )\\=\frac{2}{2\cdot a-1}-2\\=\frac{4-2\cdot a}{2\cdot a-1}\neq|a|-2

3.

f(a)=5+a^{2} , g(a)=\sqrt{a-5} -2\\gof(a)=g(5+a^{2} )\\=\sqrt{5+a^{2}-5 } -2\\=\sqrt{a^{2} } -2\\=|a|-2

4.

f(a)=3-3\cdot a , g(a)=4\cdot a-5\\gof(a)=g(3-3\cdot a )\\=4(3-3\cdot a)-5\\=7-12\cdot a\neq|a|-2

Hence, the Option 3 is correct


tia_tia [17]3 years ago
5 0
None of the pairs will deliver (g×f)(a). If you intend (g∘f)(a), then ...

... selection 3 is appropriate.

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If three quarters of a number decreased by twenty is equal to eighty two, what is that number?
Studentka2010 [4]

A number is :

x

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Three quarters of it means :

\frac{3}{4}x \\

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Decrease by 20 means :

\frac{3}{4}x - 20 \\

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Equals to 82 means :

\frac{3}{4}x - 20 = 82 \\

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What is that number ?

x asked so we must solve the above equation for x.

Let's do it....

\frac{3}{4}x - 20 = 82 \\

Plus sides 20

\frac{3}{4}x = 82 + 20 \\

\frac{3}{4}x = 102 \\

Multiply sides by 4

3x = 102 \times 4

Divided sides by 3

x =  \frac{102 \times 4}{3} \\

x =  \frac{102}{3} \times 4 \\

Simplify

x = 34 \times 4

x = 136

So that number is 136 .

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And we're done.

Thanks for watching buddy good luck.

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