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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

Please explain in detail I am very confused about the whole thing thx for ur help in advance :)

User Mbjoseph
by
8.7k points

1 Answer

2 votes

Given:


(g\circ f)(a)=|a|-2

To find:

The functions f(x) and g(x).

Solution:

We know that,


(g\circ f)(a)=g[f(a)]

If
f(a)=a^2-4 and
g(a)=√(a), then


(g\circ f)(a)=g[a^2-4]


(g\circ f)(a)=√(a^2-4)\\eq |a|-2

Option A is incorrect.

If
f(a)=(1)/(2)a-1 and
g(a)=2a-2, then


(g\circ f)(a)=g[(1)/(2)a-1]


(g\circ f)(a)=2((1)/(2)a-1)-2


(g\circ f)(a)=a-2-2


(g\circ f)(a)=a-4\\eq |a|-2

Option B is incorrect.

If
f(a)=5+a^2 and
g(a)=√(a-5)-2, then


(g\circ f)(a)=g[5+a^2]


(g\circ f)(a)=√(5+a^2-5)-2


(g\circ f)(a)=√(a^2)-2


(g\circ f)(a)=|a|-2

Option C is correct.

If
f(a)=3-3a and
g(a)=4a-5, then


(g\circ f)(a)=g[3-3a]


(g\circ f)(a)=4(3-3a)-5


(g\circ f)(a)=12-12a-5


(g\circ f)(a)=7-12x\\eq |a|-2

Option D is incorrect.

Therefore, the correct option is C.

User Xcalibur
by
8.2k points
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