Find $(f \circ g) (x)$ and $(g \circ f) (x)$ and the domain of each.
$f (x) = x + 3, g (x) = 2 x^{2} - 5 x - 3$
$(f \circ g) (x) = 2 x^{2} - 5 x - 3$ (Simplify your answer.)

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Answer

$(f \circ g) (x) = 2 x^{2} - 5 x$

Steps

Step 1 ： $(f \circ g) (x) = f (g (x))$

Step 2 ： $f (g (x)) = (2 x^{2} - 5 x - 3) + 3$

Step 3 ： $(f \circ g) (x) = 2 x^{2} - 5 x$