Question

For which pair of functions is mc004-1.j p g ? Thank you

Answer 1

C.
`f(a) = 5+a^(2)` and
`g(a) = √(a-5) -2`

Explanation:

We are given with four pair of options having functions and are required to find out which pair satisfies gоf(a) = |a| - 2.

Now, the pair that satisfies this equation is
`f(a) = 5+a^(2)` and
`g(a) = √(a-5) -2`.

i.e. gοf(a) = g(f(a)) = g(
`5+a^(2)`)

i.e. gοf(a) =
`\sqrt{5+a^(2) -5} -2`

i.e. gοf(a) =
`\sqrt{a^(2) } -2`

i.e. gοf(a) = |a|-2.

Hence, option third
`f(a) = 5+a^(2)` and
`g(a) = √(a-5) -2` is correct.

Answer 2

Consider the functions

`f(a)=5+a^(2) and g(a) = √(a-5) -2`

Now, g ₀ f (a) = g(f(a))

`g(f(a)) = g(5+a^(2) )`

`=\sqrt{5+a^(2) -5} -2`

`=|a| - 2`

Hence, the pair of functions that satisfies g ₀ f (a) = |a| - 2 are
`f(a) = 5+a^(2)` and
`g(a) = √(a-5)-2`.