$1 \leftarrow \quad$ Given $f(x)=|x|$ and $g(x)=\frac{5}{x^{2}+1}$, find the following expressions.
(a) $(f \circ g)(4)$
(b) $(g \circ f)(2)$
(c) $(f \circ f)(1)$
(d) $(g \circ g)(0)$
(a) $(f \circ g)(4)=\frac{5}{17} \quad$ (Type an integer or a simplified fraction.)
(b) $(g \circ f)(2)=1$ (Type an integer or a simplified fraction.)
(c) $(f \circ f)(1)=\square$ (Type an integer or a simplified fraction.)
Answer
Final Answer: $(f \circ f)(1)=\boxed{1}$
Step 1 ：Given $f(x)=|x|$ and $g(x)=\frac{5}{x^{2}+1}$, find the following expressions.
Step 2 ：For (a) $(f \circ g)(4)$, we substitute 4 into $g(x)$ and then the result into $f(x)$, which gives us a result of $\frac{5}{17}$.
Step 3 ：For (b) $(g \circ f)(2)$, we substitute 2 into $f(x)$ and then the result into $g(x)$, which gives us a result of 1.
Step 4 ：For (c) $(f \circ f)(1)$, we substitute 1 into $f(x)$ and then the result back into $f(x)$, which gives us a result of 1.
Step 5 ：Final Answer: $(f \circ f)(1)=\boxed{1}$
