$1 \leftarrow \quad$ 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.)

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: $(f \circ f)(1)=\boxed{1}$