Mathematics: For which pair of function is (g*f)(a)=|a|-2 1. f(a)=a^2-4 and g(a)= sqaureroot a 2. f(a)= 1/2a-1 and g(a)=2a-2 3. f(a)=5+a^2 and g(a) = sqaureroot (a-5)-2 4.f(a) =3 -3a and g(a)=4a-5

Step-by-step explanation:0.1269357705...

For which pair of function is (g*f)(a)=|a|-2 1.

harding6698

15.03.2022

The correct pair is 3

Step-by-step explanation:

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

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

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

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

Hence, the Option 3 is correct

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