Solving Function Expressions h(x): (x+a)2 +b & h-1 Range

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Discussion Overview

The discussion revolves around solving the function expression h(x) defined as h : x x 2 – 8x – 9 for x ≥ 4. Participants explore rewriting the function in the form (x+a)² + b, expressing the inverse function h⁻¹, and determining the range of h.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • Post 1 presents the function h and poses three questions regarding its form, inverse, and range.
  • Post 2 questions the notation used in Post 1, suggesting that "x x 2" should be $x^2$ and proposes completing the square to rewrite the function.
  • Post 2 provides a method for completing the square, resulting in the expression (x-4)² - 25.
  • Posts 3, 4, 5, 6, and 7 focus on how to write the notation for x², with participants discussing the use of LaTeX for formatting mathematical expressions.
  • Post 8 inquires about marking the thread as solved, indicating a potential desire for closure on the topic.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the initial function notation and engage in a discussion about the correct way to write mathematical expressions. There is no consensus on the completion of the square or the range of the function.

Contextual Notes

There are unresolved questions about the initial function notation and the assumptions regarding the use of LaTeX for mathematical expressions.

Who May Find This Useful

Students or individuals interested in function expressions, mathematical notation, and the use of LaTeX for formatting equations.

Help seeker
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The function h is defined as h : x x 2 – 8x – 9 where x ≥4
(a) h(x) can be written in the form (x+a) 2 +b, find the value of ‘a’ and ‘b’
(b) Express the inverse function h –1 in the form h –1 : x ...
(c) Find the range of function ‘h’.
 
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"x x 2"?? Was that supposed to be $x^2$, which can be written, in AASCI, as x^2? And is "(x+ a)" supposed to be $(x+ 2)^2$?

If so COMPLETE THE SQUARE! Half of -8 is -4 and $(-4)^2$ is 16. Add and subtract 16:
$x^2- 8x+ 16- 16- 9= (x^2- 8x+ 16)- 25= (x- 4)^2- 25$.
 
how do u write x^2

??
 
Help seeker said:
how do u write x^2

??

x squared

in Latex, typing \$x^2\$ yields $x^2$
 
$x^2$
 
If you are asking about how to write that $x^2$, that uses "Latex". Latex has to be installed on the board- it is on all those that I know. On this board, you start and end any Latex with a dollar sign, \$ or with "math" and "\math" inside [ ]. To get $x^2$ write "dollar sign x^2 dollar sign". Unfortunately that varies from board to board. Some use and.
 
Last edited:
$x^2$
 
How do I mark as solved?
 

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