Given $f(x)=3x+2$ and $g(x)=2x^2-1$ find the following and state if the composite function exists.
$$(f\circ g)(x)=f(g(x))$$
$$f(2x^2-1)=3x+2$$
$$(f\circ g)(x)=3(2x^2-1)+2$$
Do I stop here? Or continue to get $6x^2 -1$?
Yes it exists.
Given $f(x)=3x+2$ and $g(x)=2x^2-1$ find the following and state if the composite function exists.
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$\begingroup$
calculus
proof-verification
1 Answers
1
It doesn't matter how much you simplify mathematically, though a teacher might care. Yes, you've calculated the composition of the functions.