Answer:
Option 3
Step-by-step explanation:
Option 1
f(a) = a² - 4
g(a) = √a
(gof)(a) = [tex]\sqrt{a^{2}-4}[/tex]
Option 2
f(a) = [tex]\frac{1}{2}a-1[/tex]
g(a) = 2a - 2
(gof)(a) = [tex]2[\frac{1}{2}a-1]-2[/tex]
= (a - 2) - 2
= a - 4
Option 3
f(a) = 5 + a²
g(a) = [tex]\sqrt{(a-5)}-2[/tex]
(gof)(a) = [tex]\sqrt{(a^2+5-5)}-2[/tex]
= |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.
