Question

Let f(x)=1/(x^2+1) and g(x)=x^-6. Find f(g(x)) and its domain.

Answer 1

I got 1/((x^-6)^2 + 1) which simplifies to x^3/(1+x^3)

Answer 2

That makes the domain all reals except for -1 the way I am looking at it, but that domain is not an option given.

Answer 3

@kropot72

Answer 4

The options for the domain are
all real numbers
x>0
x is not equal to 0
x is greater than or equal to 0

Answer 5

Is it all real numbers since the powers were originally even?

Answer 6

I thought the domain had to be real at each step though.

Answer 7

\[f(x)=\frac{1}{x^2+1} \text{ and we have } g(x)=x^{-6} \text{ aka } g(x)=\frac{1}{x^6}\]

Answer 8

Right.

Answer 9

so notice the domains of f and g separately first

Answer 10

the domain of f is all real numbers
but what is the domain of g?

--
and also I'm having trouble seeing how you got your f(g(x)) anyways

Answer 11

Domain of g is anything but 0

Answer 12

right @JoannaBlackwelder

Answer 13

so we already know we can't include 0 in the domain of f(g(x))

Answer 14

right so you should have