Question

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

Answer 1

Consider the functions

$f(a)=5+a^{2} and g(a) = \sqrt{a-5} -2$

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 $g(a) = \sqrt{a-5}-2$.

Answer 2

Answer:

C. $f(a) = 5+a^{2}$ and $g(a) = \sqrt{a-5} -2$

Step-by-step 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 $g(a) = \sqrt{a-5} -2$.

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 $g(a) = \sqrt{a-5} -2$ is correct.