November 25th, 2017, 11:24 AM  #1 
Newbie Joined: Oct 2017 From: Rumba Posts: 20 Thanks: 0  Calculating function How do i do this? 
November 25th, 2017, 12:22 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,979 Thanks: 1026 
a) $g \circ f = g(f(x))$ The domain of $g \circ f$ is the same as the domain of $f(x)$ and it's range is the same as $g(x)$ $(g \circ f)(1) = g(f(1)) = g(a) = 50$ you go ahead and find the rest of them b) $f^{1}$ is defined such that $f^{1}(f(x)) = f(f^{1}(x))=x$ so for example $f^{1}(f(1))=f^{1}(a) = 1$ so $f^{1}:\{(a,1),\dots \}$ you figure out the rest of the entries and the domain and range. It should be pretty clear that the domain of $f^{1}$ is the equal to the range of $f$ and vice versa. c) is trivial $(h+i)(x) = h(x)+i(x) = x^2 + 2x + 4 = (x+1)^2 + 3$ I leave it to you to determine the domain and range. 

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