If $f(x)=2 x-1$ and $g(x)=x+8$, find $(f \circ g)(x)$ and $(g \circ f)(x)$
$(f \circ g)(x)=$
$(g \circ f)(x)=$

Step 1 ：The question is asking for the composition of two functions, $f(x)$ and $g(x)$. The composition of functions is a concept in mathematics where you apply one function to the result of another function. In this case, we are asked to find $(f \circ g)(x)$ and $(g \circ f)(x)$.

Step 2 ：For $(f \circ g)(x)$, this means we apply the function $g(x)$ first and then apply the function $f(x)$ to the result. So, we substitute $g(x)$ into $f(x)$.

Step 3 ：For $(g \circ f)(x)$, this means we apply the function $f(x)$ first and then apply the function $g(x)$ to the result. So, we substitute $f(x)$ into $g(x)$.

Step 4 ：Given that $f(x) = 2x - 1$ and $g(x) = x + 8$, we can substitute $g(x)$ into $f(x)$ to get $(f \circ g)(x) = 2(x + 8) - 1 = 2x + 15$.

Step 5 ：Similarly, we can substitute $f(x)$ into $g(x)$ to get $(g \circ f)(x) = (2x - 1) + 8 = 2x + 7$.

Step 6 ：So, the final answers are $(f \circ g)(x) = \boxed{2x + 15}$ and $(g \circ f)(x) = \boxed{2x + 7}$.