Question

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

Answer 1

None of the pairs will deliver (g×f)(a). If you intend (g∘f)(a), then ...

... selection 3 is appropriate.

Answer 2

The correct pair is 3

Explanation:

1.

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

2.

`f(a)=(1)/(2\cdot a-1), g(a)=2\cdot a -2\\gof(a)=g((1)/(2\cdot a-1) )\\=(2)/(2\cdot a-1)-2\\=(4-2\cdot a)/(2\cdot a-1)\\eq|a|-2`

3.

`f(a)=5+a^(2) , g(a)=√(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\\eq|a|-2`

Hence, the Option 3 is correct