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

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SUMMARY

The function h is defined as h(x) = x² - 8x - 9 for x ≥ 4. By completing the square, it can be rewritten in the form h(x) = (x - 4)² - 25, identifying a = -4 and b = -25. The inverse function h⁻¹ can be expressed as h⁻¹(x) = 4 ± √(x + 25). The range of the function h is determined to be [-25, ∞).

PREREQUISITES
  • Understanding of quadratic functions and their properties
  • Knowledge of completing the square technique
  • Familiarity with inverse functions
  • Basic proficiency in LaTeX for mathematical notation
NEXT STEPS
  • Study the method of completing the square in quadratic equations
  • Learn how to derive inverse functions for various types of functions
  • Explore the concept of function ranges and their implications
  • Practice writing mathematical expressions in LaTeX
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Students studying algebra, mathematics educators, and anyone interested in mastering quadratic functions and their inverses.

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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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