8x + 15 G(x) = X - 3 H(x) = F(x) ÷g(x) H(x)=? And What Is The Domain Of ...

Subject ZIP Search Search Find an Online Tutor Now Ask Ask a Question For Free Login F(x) Questions f(x) = x2 - 8x + 15 g(x) = x - 3 h(x) = f(x) ÷g(x) h(x)=? and what is the domain of h(x) what is the value of h(x), and what is the domain of h(x)? Follow • 2 Add comment More Report

1 Expert Answer

Best Newest Oldest By: Best Newest Oldest If I'm reading your equations correctly, they are: f(x)=x2-8x+15 g(x)=x-3 h(x)=f(x)/g(x) The domain of a function is the set of all possible inputs, what we can plug in for our variable. The largest two limitations on domains (other than explicit limitations, like in piecewise functions) are radicals and rational functions. With radical expressions we know that we CANNOT take an even root of a negative number. I don't see that problem here. With rationals we know that we CANNOT divide by zero. So the question becomes, when does h(x) ask us to divide by zero? When is the denominator of h(x) zero? Since the denominator of h(x) is g(x), we cannot let g(x) equal zero. So when does that happen? when x-3=0 or when x=3. I hope you see here that if x=3, then g(x)=0, and so h(x)=f(x)/0, which we CANNOT do. The domain of h(x) is all real numbers not equal to 3. There is more going on here. If you had factored f(x) first, you could have written h(x) in a confusing way: h(x)=( f(x) ) / ( g(x) ) h(x)= ( (x-5)(x-3) ) / (x-3) Right here, it looks like (x-3) will cancel out from the top and bottom of your fraction. It does, in a way. The graph of h(x) will behave exactly like the line y=x-5, except that it has a hole in it at x=3 (check this! it's cool!) SOOO, the takeaway is that it is better to determine limitations on your domain BEFORE over-simplifying your equations. Upvote • 0 Downvote Add comment More Report

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem. Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.

¢ € £ ¥ ‰ µ · • § ¶ ß ‹ › « » < > ≤ ≥ – — ¯ ‾ ¤ ¦ ¨ ¡ ¿ ˆ ˜ ° − ± ÷ ⁄ × ƒ ∫ ∑ ∞ √ ∼ ≅ ≈ ≠ ≡ ∈ ∉ ∋ ∏ ∧ ∨ ¬ ∩ ∪ ∂ ∀ ∃ ∅ ∇ ∗ ∝ ∠ ´ ¸ ª º † ‡ À Á Â Ã Ä Å Æ Ç È É Ê Ë Ì Í Î Ï Ð Ñ Ò Ó Ô Õ Ö Ø Œ Š Ù Ú Û Ü Ý Ÿ Þ à á â ã ä å æ ç è é ê ë ì í î ï ð ñ ò ó ô õ ö ø œ š ù ú û ü ý þ ÿ Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ φ χ ψ ω ℵ ϖ ℜ ϒ ℘ ℑ ← ↑ → ↓ ↔ ↵ ⇐ ⇑ ⇒ ⇓ ⇔ ∴ ⊂ ⊃ ⊄ ⊆ ⊇ ⊕ ⊗ ⊥ ⋅ ⌈ ⌉ ⌊ ⌋ 〈 〉 ◊

RELATED TOPICS

Algebra 1 Algebra Equation Functions Simplify College Algebra Function Standard Form Variables Algebra Word Problem ... F(x) Quadratic Word Problem Solution Sets Degree Operations Evaluate Function Operation College Math Functions Word Problem Intermediate Alegbra

RELATED QUESTIONS

solve for x

Answers · 3

f(x)=x^2+3 upward 15 unit

Answers · 1

Given functions f and g, perform the indicated operations:

Answers · 5

Evaluate and simplify the following function:

Answers · 2

Need help with two function questions. Let f(x)=9+x+x^2. 1. Find f(x + h). 2. Find f(x+h)-f(x)/h and simplify

Answers · 3

RECOMMENDED TUTORS

Zavier A.

5.0 (424)

Evan W.

5.0 (1,959)

Erika T.

5.0 (1,236) See more tutors

find an online tutor

• Differential Equations tutors
• Precalculus tutors
• AP Calculus AB tutors
• Complex Analysis tutors
• Linear Programming tutors
• Multivariable Calculus tutors
• AP Calculus tutors
• Algebra 2 tutors