Question

(Plz answer I am time)
For which pairs of function is (g*f)(a)=|a|-2​

Answer 1

Option 3

Explanation:

Option 1

f(a) = a² - 4

g(a) = √a

(gof)(a) =
`\sqrt{a^(2)-4}`

Option 2

f(a) =
`(1)/(2)a-1`

g(a) = 2a - 2

(gof)(a) =
`2[(1)/(2)a-1]-2`

= (a - 2) - 2

= a - 4

Option 3

f(a) = 5 + a²

g(a) =
`√((a-5))-2`

(gof)(a) =
`√((a^2+5-5))-2`

= |a| -2

Option 4

f(a) = 3 - 3a

g(a) = 4a - 5

(gof)(a) = 4(3 - 3a) - 5

= 12 - 12a - 5

= 7 - 12a

Therefore, Option 3 is the answer.