SOLUTION: Using the function f(x)=x^2+x and g(x)=x-5 a. Find h(x)=(f◦g)(x). b. State the domain of h(x)=f◦g)(x). c. Find h(x)=(g◦f)(x). d. State the domain of h(x)=(g&#

Algebra ->  Graphs -> SOLUTION: Using the function f(x)=x^2+x and g(x)=x-5 a. Find h(x)=(f◦g)(x). b. State the domain of h(x)=f◦g)(x). c. Find h(x)=(g◦f)(x). d. State the domain of h(x)=(g&#      Log On


   

Question 394131: Using the function f(x)=x^2+x and g(x)=x-5
a. Find h(x)=(f◦g)(x).
b. State the domain of h(x)=f◦g)(x).
c. Find h(x)=(g◦f)(x).
d. State the domain of h(x)=(g◦f)(x).
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Using the function f(x)=x^2+x and g(x)=x-5
a. Find h(x)=(f◦g)(x).
fog(x) = f[x-5]= (x-5)^2+(x-5) = x^2-10x+25+x-5 = x^2-9x+20
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b. State the domain of h(x)=f◦g)(x).
The domain of g is All Real Numbers
The range that g produces is All Real Numbers
So the domain of f is All Real Numbers
Conclusion: The domain of fog(x) is All Real Numbers
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c. Find h(x)=(g◦f)(x)= g[x^2+x] = x^2+x-5
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d. State the domain of h(x)=(g◦f)(x).
The domain of f is R
The Range of f is >=-1/4
So the domain of g is >=-1/4
Conclusion: The domain of gof(x) is x>=-1/4
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Cheers,
Stan H.