Abbygail R. answered • 05/16/19
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( f o g ) (x)= 2 (radical x+3)^2 -3
I substituted g into f(x).
=2(x+3) - 3
=2x+6-3
=2x+3 {Ans}
Domain for all linear functions is all real number.
Abbygail R.
tutor
Hi Britzel!
So since square root and squaring are opposing operations they cancel each other out only leaving what is under the radical.
As for the domain of the answer (2x+3), a linear function with no restrictions will have a domain of all real numbers meaning negative infinity to positive infinity.
f(x) = 2x^2-3 *Domain is also all real numbers*
g(x) = radical x+3 *For a radical function the domain is not all real numbers. The function is restricted to what value of x will make the total value under the radical greater than or equal to zero. This is because you cant square root a negative number to get a real value.
So to find the domain of g(x) = radical x+3
Set x+3 >= 0 (>= means greater than or equal to)
Solve x>= -3
So domain is [-3, infinity).
Let me know if you need more help on finding domains!
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05/16/19
Britzel S.
thank you! your answer is correct, only one question what happened to the radical? Also, do you know how to find it's domain?05/16/19