Question 937972: hey there,
I'm struggling with a bit of university pre calc this is an activity i have been given for practice for an upcoming test and would really appreciate a step by step in how you do all these examples, our teacher seemed to rush through it and it makes no sense to me
let f(x) = ln(x), g(x) = √x + 1 and h(x) 1/x, be defined on their natural domains. Define the following functions and state the domain for each function, using set notation
(a) (f o g)(x)
(b)(g o f)(x)
(c) g(x)h(x)
thanks
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! let f(x) = ln(x), g(x) = √x + 1 and h(x) 1/x, be defined on their natural domains. Define the following functions and state the domain for each function, using set notation
(a)(f o g)(x) = f[g(x)] = f[sqrt(x)+1] = ln[sqrt(x)+1]
Domain: x >= 0
Range:: y >= 0
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(b)(g o f)(x) = g[f(x)] g[ln(x)] = sqrt[ln(x)+1]
Domain: x >= 0
Range: y >= 1
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(c) g(x)h(x) = (sqrt(x)+1)(1/x) = [sqrt(x)+1]/x
Domain: x > 0
Range: ?
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Cheers,
Stan H.
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