Find the following f ( x ) = x 2 − 16 , ...

Darian Hubbard

Darian Hubbard

Answered

2022-07-22

Find the following
f ( x ) = x 2 16 ,     g ( x ) = x 2 x 2 + 1
a ) ( f + g ) ( x ) = b ) ( f g ) ( x ) = c ) ( f g ) ( x ) = d ) ( f / g ) ( x ) =
What is the domain of f/g?

Answer & Explanation

neobuzdanio

neobuzdanio

Expert

2022-07-23Added 13 answers

f ( x ) = x 2 16 ,     g ( x ) = x 2 x 2 + 1 a ) ( f + g ) ( x ) = f ( x ) + g ( x ) = x 2 16 + x 2 x 2 + 1 b ) ( f g ) ( x ) = f ( x ) g ( x ) = x 2 16 x 2 x + 1 c ) ( f g ) ( x ) = f ( x ) g ( x ) = x 2 16 x 2 ( x 2 + 1 ) = x 2 x 2 16 x 2 + 1 d ) ( f / g ) ( x ) = f ( x ) g ( x ) = x 2 16 x ( x 2 + 1 ) = x 2 16 ( x 2 + 1 ) x 2
For domain of (f/g)(x)
x 2 0
x 0 (i)
and
x 2 16 0 ( x + 4 ) ( x 4 ) 0 x ( , 4 ] , [ 4 , ) (ii)
From (i) and (ii)
Domain of f / g ( , 4 ] , [ 4 , )

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