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November 25th, 2017, 12:24 PM   #1
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Calculating function

How do i do this?
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November 25th, 2017, 01:22 PM   #2
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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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