Question

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

Answer 1

C

Explanation:

edge2020

Answer 2

f(a) = 5 + a² and g(a) = √(a - 5) - 2

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.