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JoannaBlackwelder
 one year ago
Let f(x)=1/(x^2+1) and g(x)=x^6. Find f(g(x)) and its domain.
JoannaBlackwelder
 one year ago
Let f(x)=1/(x^2+1) and g(x)=x^6. Find f(g(x)) and its domain.

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JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0I got 1/((x^6)^2 + 1) which simplifies to x^3/(1+x^3)

JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0That makes the domain all reals except for 1 the way I am looking at it, but that domain is not an option given.

JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0The options for the domain are all real numbers x>0 x is not equal to 0 x is greater than or equal to 0

JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0Is it all real numbers since the powers were originally even?

JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0I thought the domain had to be real at each step though.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[f(x)=\frac{1}{x^2+1} \text{ and we have } g(x)=x^{6} \text{ aka } g(x)=\frac{1}{x^6}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so notice the domains of f and g separately first

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the 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

JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0Domain of g is anything but 0

freckles
 one year ago
Best ResponseYou've already chosen the best response.1right @JoannaBlackwelder

JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441048089386:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so we already know we can't include 0 in the domain of f(g(x))

freckles
 one year ago
Best ResponseYou've already chosen the best response.1right so you should have dw:1441134566849:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and you can get rid of the negative exponents by multiplying top and bottom by x^(12)

JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0Oh, duh! I don't know what I was thinking. Thank you!

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0My simplification is: \[\large \frac{1}{(x^{6})^{2}+1}=\frac{x^{12}}{1+x^{12}}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you do understand the domain is all real numbers but x=0 right?

JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, I got it now. Thanks so much, both of you! :)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1this is because g(x) did not exist at x=0 you originally have \[f(g(x))=\frac{1}{(\frac{1}{x^6})^{2}+1} \\ \text{ and pluggin \in 0 into this makes that } \\ \text{ one little fraction undefined }\]
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