Given f(x)=1/x^2−4 & g(x)=1/x−2 a) find g(f(x)) b) State a suitable domain

engausidarb

engausidarb

Answered question

2022-09-09

Given f ( x ) = 1 x 2 4 & g ( x ) = 1 x 2
a) find g ( f ( x ) )
b) State a suitable domain

Answer & Explanation

Willie Smith

Willie Smith

Beginner2022-09-10Added 18 answers

To compute g ( f ( x ) ) (let's call it h ( x ) you take
y = 1 x 2 4
and replace that on g, yelding
g ( y ) = 1 1 x 2 4 2 = x 2 4 2 = x 2 6
As for the domain, this new function h is defined for all x R .
ubumanzi18

ubumanzi18

Beginner2022-09-11Added 2 answers

Even though the composite can be defined for all x R , plugging x = 2 through the composite function does not make sense.

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