1 Answer

PiRK · Answer 1 · 2023-03-13T09:53:32+0000

ANSWERS

a) Domain: x ∈ (-∞, -1) ∪ (-1, ∞)

b) Domain: x ∈ (-∞, 0) ∪ (0, ∞)

Step-by-step explanation

These compositions are:

a)

$f\circ g=f(g(x))=(2)/(g(x))=(2)/(x+1)$

And

b)

$g\circ f=g(f(x))=f(x)+1=(2)/(x)+1$

To find the domain in each function we have to find the values that x cannot take. If there aren't any, then the domain is all real values.

For composition a) note that x is in the denominator as (x+1). As we know, for real numbers the denominator can't be 0, so that's our restriction:

$x+1\\e0$

Solving for x:

$x\\e-1$

The domain for f º g is all real values except x = -1

For composition b) we have x in the denominator too, but it is alone. Therefore, as said before, x cannot be 0.

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