Find $$ (f \circ g)(x) $$ and $$ (g \circ f)(x) $$ for the pair of functions. $$ f(x)=x^{2}+4 x, \quad g(x)=7 x+1 $$ $$ (f \circ g)(x)=\square $$ $$ (g \circ f)(x)=\square $$

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**Step 1: Compute $$(f \circ g)(x)$$**

- Given $$ g(x)=7x+1 $$, substitute it into $$ f(x)=x^2+4x $$:
  
  $$
  (f \circ g)(x)=f(g(x))=(7x+1)^2+4(7x+1)
  $$

- Expand $$ (7x+1)^2 $$:

$$
  (7x+1)^2 = 49x^2+14x+1
  $$

- Expand $$ 4(7x+1) $$:

$$
  4(7x+1)=28x+4
  $$

- Combine the results:

$$
  (f \circ g)(x)=49x^2+14x+1+28x+4
  $$
  
- Simplify by combining like terms:

$$
  (f \circ g)(x)=49x^2+(14x+28x)+(1+4)=49x^2+42x+5
  $$

**Step 2: Compute $$(g \circ f)(x)$$**

- Given $$ f(x)=x^2+4x $$, substitute it into $$ g(x)=7x+1 $$:

$$
  (g \circ f)(x)=g(f(x))=7(x^2+4x)+1
  $$

- Distribute the $$ 7 $$:

$$
  7(x^2+4x)=7x^2+28x
  $$

- Combine with the constant:

$$
  (g \circ f)(x)=7x^2+28x+1
  $$

**Final Answers:**

$$
(f \circ g)(x)=49x^2+42x+5
$$

$$
(g \circ f)(x)=7x^2+28x+1
$$
$$ (f \circ g)(x) = 49x^2 + 42x + 5 $$ $$ (g \circ f)(x) = 7x^2 + 28x + 1 $$

Find and for the pair of functions.

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