SOLUTION: If f(x)=2x^2 +5 and g(x)=sqrt(x-5) then find the domain and range of (fog)x?

Question 606204: If f(x)=2x^2 +5 and g(x)=sqrt(x-5)
then find the domain and range of (fog)x?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If f(x)=2x^2 +5 and g(x)=sqrt(x-5)
then find the domain and range of (fog)x?
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fog(x) = f[g(x)] = f[sqrt(x-5)]
----
= 2(sqrt(x-5))^2 + 5
---
= 2(x-5) + 5
---
= 2x-5
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Domain: Since g(x) = sqrt(x-5), domain is "All Real Numbers >= 5"
Then range of g(x) = "All Real Numbers >= 0":
------------------------------
So Ddomain of fog(x) = "All Real Numbers >= 0:
Range of fog(x): Since f(x) = 2x^2+5, range is "All Real Numbers
>= 5".
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Cheers,
Stan H.
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