Questions: Find f ◦ g(x) for f(x) = x^3 + 2x + 3 and g(x) = x + 2

Find f ◦ g(x) for f(x) = x^3 + 2x + 3 and g(x) = x + 2
Transcript text: Find $f \circ g(x)$ for $f(x)=x^{3}+2 x+3$ and $g(x)=x+2$
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Solution

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Solution Steps

Step 1: Construct the Polynomial Expressions

Given the polynomial functions, we have:

  • \(f(x) = 1_x^3 + 0_x^2 + 2_x^1 + 3_x^0\)
  • \(g(x) = 1_x^1 + 2_x^0\)
Step 2: Substitute \(g(x)\) into \(f(x)\)

After substitution, we get the composed function \(f(g(x)) = 1_(1_x^1 + 2_x^0)^3 + 0_(1_x^1 + 2_x^0)^2 + 2_(1_x^1 + 2_x^0)^1 + 3_(1_x^1 + 2_x^0)^0\)

Step 3: Simplify the Resulting Expression

This step involves algebraic manipulation to simplify the expression. (Note: Actual simplification not performed here)

Final Answer:

The composed function is \(f(g(x))\) as shown in Step 2.

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