For which pair of functions is (g circle f) (a) = StartAbsoluteValue a EndAbsoluteValue minus 2? f (a) = a2 - 4 and g (a) = StartRoot a EndRoot f (a) = one-half a minus 1 and g (a) = 2a - 2 f (a) = 5 + a2 and g (a) = StartRoot a minus 5 EndRoot minus 2 f (a) = 3 - 3a and g (a) = 4a - 5

f (a) = 5 + a² and g (a) = √ (a - 5) - 2

Step-by-step explanation:

(g°f) (a) means that g (a) has to be evaluated at f (a), that is, replace a in g (a) with f (a).

Taking:

f (a) = 5 + a² and g (a) = √ (a - 5) - 2

we get:

(g°f) (a) = √ (5 + a² - 5) - 2 = √ (a²) - 2 = |a| - 2

Where the theorem that states:

for any real number a, √ (a²) = |a|

was used.