Question 618186: Hello, can someone please help me..I cannot wrap my head around this problem.
if f(x)=ln x, g(x)=e^(7x), and h(x)=x^6 find the following
1. (fog)(x) and domain of (fog)(x)
2. (gof)(x) and domain of (gof)(x)
3. (fog)(x) and domain of (foh)(x)
I tried to start them out but I am completely stumped!
1). (fog)(x)=f(g)x))= lnx(e^(7x))
2). (gof)(x)=g(f(x))=e^(7x)lnx))
3.) (foh)(x)=f(h)x))=lnx(x^6)
I can usually figure out the composite functions but the exponential and logarithm has me really confused.
Thanks a ton!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! if f(x)=ln x, g(x)=e^(7x), and h(x)=x^6 find the following
1. (fog)(x) and domain of (fog)(x)
2. (gof)(x) and domain of (gof)(x)
3. (fog)(x) and domain of (foh)(x)
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Answers:
1). (fog)(x)=f(g(x))= f(e^(7x)) = ln(e^(7x)) = 7x
Domain: All Real Numbers
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2). (gof)(x)=g(f(x))= g(ln(x)) = e^(7ln(x)) = e^(ln(x^7)) = x^7
Domain: All Real Numbers greater than zero.
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3.) (foh)(x)= f(h(x))=f(x^6) = ln(x^6) = 6ln(x)
Domain: All Real Numbers greater than zero.
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Cheers,
Stan H.
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