Given :f(x)=x2+5x+6 and h(x)=x+2  find the following (h-f)(x)

To find \((h - f)(x)\), we need to subtract \(f(x)\) from \(h(x)\).

Given functions:
\[
f(x) = x^2 + 5x + 6
\]
\[
h(x) = x + 2
\]

Now, calculate \((h - f)(x)\):
\[
(h - f)(x) = h(x) - f(x)
\]

Substituting the values of \(h(x)\) and \(f(x)\):
\[
(h - f)(x) = (x + 2) - (x^2 + 5x + 6)
\]

Simplify by distributing the negative sign:
\[
(h - f)(x) = x + 2 - x^2 - 5x - 6
\]

Combine like terms:
\[
(h - f)(x) = -x^2 - 4x - 4
\]

So, \((h - f)(x) = -x^2 - 4x - 4\).

Would you like to see details or have any questions? Here are some related questions:

1. How do you find \((f + h)(x)\) for the given functions?
2. What is \((f \times h)(x)\)?
3. Can you find the domain of the function \((h - f)(x)\)?
4. How do you find \((h \div f)(x)\) and simplify it?
5. What are the roots of \((h - f)(x) = 0\)?

**Tip:** When combining functions, carefully distribute any negative signs and combine like terms correctly to avoid errors.

Given: f(x)=x^2+5x+6 and h(x)=x+2, find the following (h-f)(x)

Explore how to subtract two functions, f(x) = x^2 + 5x + 6 and h(x) = x + 2, to find (h - f)(x). This problem demonstrates essential algebraic concepts, including function subtraction and polynomial manipulation, suitable for Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation