Find $(f \circ g) (x)$ and $(g \circ f) (x)$ and the domain of each.
$f (x) = x + 17, g (x) = x - 17$
$(f \circ g) (x) = x$ (Simplify your answer.)
$(g \circ f) (x) = x$ (Simplify your answer.)
The domain of $(f \circ g) (x)$ is
(Type your answer in interval notation.)

Answer

Expert–verified

Hide Steps

Answer

The domain of $(f \circ g) (x)$ and $(g \circ f) (x)$ is $(- \infty, \infty)$

Steps

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

Step 2 ： $(f \circ g) (x) = f (x - 17) = (x - 17) + 17$

Step 3 ： $(f \circ g) (x) = x$

Step 4 ： $(g \circ f) (x) = g (f (x))$

Step 5 ： $(g \circ f) (x) = g (x + 17) = (x + 17) - 17$

Step 6 ： $(g \circ f) (x) = x$

Step 7 ：The domain of $(f \circ g) (x)$ and $(g \circ f) (x)$ is $(- \infty, \infty)$