Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
3. Functions
Function Operations
Problem 38Blitzer - 8th Edition
Textbook Question
Find f+g, f−g, fg, and gf. Determine the domain for each function.
f(x)=5−x2, g(x)=x2+4x−12
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Step 1: To find , add the functions and . This means you will add and . Combine like terms to simplify.
Step 2: To find , subtract from . This involves subtracting from . Again, combine like terms to simplify.
Step 3: To find , multiply the functions and . This requires distributing across and combining like terms.
Step 4: To find , divide by . This means writing . Simplify if possible, and identify any restrictions on the domain where the denominator is zero.
Step 5: Determine the domain for each function. For and , the domain is all real numbers. For , the domain is also all real numbers. For , exclude values that make the denominator zero by solving to find the restricted values.
Recommended similar problem, with video answer:
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Related Practice
Textbook Question
Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2
(ƒ+g)(2)
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