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

In summary, the function h is defined as h : x x 2 - 8x - 9 where x ≥4. It can be written in the form (x+a) 2 +b, and the values of 'a' and 'b' can be found using the process of completing the square. The inverse function h -1 can be expressed as h -1 : x ... and the range of function h can be found by substituting different values of x. In Latex, typing x^2 yields $x^2$.
  • #1
Help seeker
15
0
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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  • #2
"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:
$x^2- 8x+ 16- 16- 9= (x^2- 8x+ 16)- 25= (x- 4)^2- 25$.
 
  • #3
how do u write x^2

??
 
  • #4
Help seeker said:
how do u write x^2

??

x squared

in Latex, typing \$x^2\$ yields $x^2$
 
  • #5
$x^2$
 
  • #6
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 [tex] and [/tex].
 
Last edited:
  • #7
$x^2$
 
  • #8
How do I mark as solved?
 

1. What is a function expression?

A function expression is a mathematical representation of a relationship between two or more variables. It is typically written as f(x), where f is the name of the function and x is the input variable.

2. How do you solve a function expression?

To solve a function expression, you need to plug in a value for the input variable, perform the necessary operations, and simplify the resulting expression. For example, to solve h(x) = (x+a)^2 + b, you would substitute a value for x, such as 3, and then simplify the expression to get the corresponding output value for h(x).

3. What is the purpose of the h-1 notation in h-1 Range?

The h-1 notation in h-1 Range indicates the inverse function of h(x). This means that the input and output values of h(x) are switched in the inverse function, and the resulting range is the set of all possible input values for h(x).

4. How do you find the range of a function expression?

The range of a function expression is the set of all possible output values. To find the range, you can either graph the function and identify the y-values, or you can solve for the output variable in terms of the input variable and determine the possible values using algebraic methods.

5. Can you explain the meaning of the variables a and b in the function expression (x+a)^2 + b?

The variable a represents a constant value that is added to the input variable x before it is squared. The variable b represents another constant value that is added to the squared result. These constants can affect the shape and position of the graph of the function, and can also determine the range of the function.

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