Let $$ f(x)=3 x+5 $$. Determine $$ (f \circ f \circ f)(x) $$ $$ (f \circ f \circ f)(x)=\square $$

Question

UpStudy AI · Accepted Answer

To determine $$(f \circ f \circ f)(x)$$, which represents applying the function $$f$$ three times in succession, follow these steps:

1. **First Application ($$f(x)$$)**:
   $$
   f(x) = 3x + 5
   $$

2. **Second Application ($$f(f(x))$$)**:
   $$
   f(f(x)) = f(3x + 5) = 3(3x + 5) + 5 = 9x + 15 + 5 = 9x + 20
   $$

3. **Third Application ($$f(f(f(x)))$$)**:
   $$
   f(f(f(x))) = f(9x + 20) = 3(9x + 20) + 5 = 27x + 60 + 5 = 27x + 65
   $$

**Final Result**:
$$
(f \circ f \circ f)(x) = 27x + 65
$$
$$(f \circ f \circ f)(x) = 27x + 65$$

Let \( f(x)=3 x+5 \). Determine \( (f \circ f \circ f)(x) \) \( (f \circ f \circ f)(x)=\square \)