Math Problem Statement

Find (h + p)(-3) where h(x) = x^2; D = {Reals}, and p(x) = x^3; D = {Negative integers}.

Solution

This problem asks to find the expression (h+p)(3)(h + p)(-3), where:

  • h(x)=x2h(x) = x^2 and D=RealsD = \text{Reals},
  • p(x)=x3p(x) = x^3 and D=Negative integersD = \text{Negative integers}.

Let’s break it down:

  1. (h+p)(x)=h(x)+p(x)(h + p)(x) = h(x) + p(x), so we have: (h+p)(x)=x2+x3.(h + p)(x) = x^2 + x^3.

  2. Now, we want to evaluate this at x=3x = -3: (h+p)(3)=(3)2+(3)3.(h + p)(-3) = (-3)^2 + (-3)^3.

  3. Calculate each part: (3)2=9and(3)3=27.(-3)^2 = 9 \quad \text{and} \quad (-3)^3 = -27.

  4. So, the result is: (h+p)(3)=9+(27)=18.(h + p)(-3) = 9 + (-27) = -18.

Thus, the value of (h+p)(3)(h + p)(-3) is 18-18.

Do you need any further clarification or details on the steps?

Here are five related questions:

  1. What happens when you evaluate (h+p)(2)(h + p)(2)?
  2. How would you solve a similar problem where p(x)=x4p(x) = x^4?
  3. What is the general form for the sum of two functions evaluated at a point?
  4. How do the domains of the functions affect the problem?
  5. What are the different ways to combine functions, such as addition and multiplication?

Tip: When evaluating sums or differences of functions, always be careful to apply the operations correctly to each function before evaluating.

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Math Problem Analysis

Mathematical Concepts

Functions
Function Evaluation
Polynomials

Formulas

(h + p)(x) = h(x) + p(x)
h(x) = x^2
p(x) = x^3

Theorems

Sum of functions

Suitable Grade Level

Grades 9-11