Question

For which pair of functions does (g∘f)(a) = |a| - 2?

A) f(x) = 2x, g(x) = |x|
B) f(x) = x^2, g(x) = |x|
C) f(x) = x^2, g(x) = 2x
D) f(x) = 2x, g(x) = x^2

Answer 1

The pair of functions f(x) = 2x and g(x) = |x| is the correct pair for (g∘f)(a) = |a| - 2. Hence, A) is correct.

Step-by-step explanation:

To find the pair of functions for which (g∘f)(a) = |a| - 2, we need to determine which pair of functions when composed together gives us the expression |a| - 2.

Let's plug in the given functions options into the expression (g∘f)(a) and simplify to see if we can find a match:

Option A) f(x) = 2x, g(x) = |x|:

(g∘f)(a) = g(f(a)) = |2a| = 2a

Option B) f(x) = x^2, g(x) = |x|:

(g∘f)(a) = g(f(a)) = |a^2| = a^2

Option C) f(x) = x^2, g(x) = 2x:

(g∘f)(a) = g(f(a)) = 2a^2

Option D) f(x) = 2x, g(x) = x^2:

(g∘f)(a) = g(f(a)) = (2a)^2 = 4a^2

From the options given, only option A) f(x) = 2x, g(x) = |x| matches the expression (g∘f)(a) = |a| - 2. Therefore, the correct pair of functions is f(x) = 2x, g(x) = |x|.