If f(x)=x²+2 and g(x)=x²+5 then the domain of the (fog) (x) is (-∞,∞).
Given the f(x)=x²+2 and g(x)=x²+5
We have to find the domain of the (fog) (x)
The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.
then,(fog) (x)= (x²+5)²+ 2
=x⁴+25+10x²+2
= x⁴+27+10x²
Now on any real value of x the value of (fog) (x) exists therefore (fog) (x) can take all the values of the real number.
So domain (fog) (x)= (-∞,∞).
Learn more about the domain here: https://brainly.com/question/26098895
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