Composition of Functions 

c ( x  ) = x+5
j ( x ) = 2x² + 3x + 2

Find : ( c o j ) (x) 

To find the composition of functions \( (c \circ j)(x) \), you need to substitute the function \( j(x) \) into the function \( c(x) \).

Given:
- \( c(x) = x + 5 \)
- \( j(x) = 2x^2 + 3x + 2 \)

The composition \( (c \circ j)(x) \) is defined as \( c(j(x)) \).

### Steps:

1. **Substitute \( j(x) \) into \( c(x) \):**
   \[
   (c \circ j)(x) = c(j(x)) = c(2x^2 + 3x + 2)
   \]
   
2. **Apply the function \( c(x) = x + 5 \):**
   \[
   (c \circ j)(x) = (2x^2 + 3x + 2) + 5
   \]
   
3. **Simplify the expression:**
   \[
   (c \circ j)(x) = 2x^2 + 3x + 7
   \]

So, the composition \( (c \circ j)(x) \) is:
\[
(c \circ j

Explore how to find the composition of functions (c o j)(x) where c(x) = x + 5 and j(x) = 2x² + 3x + 2. This detailed guide provides step-by-step instructions on substituting and simplifying functions to solve compositions. Suitable for students in Grades 10-12.

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