- #1
JBauer
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f(x) = third square root of |x^2 - 9| - 3
I need set everything = to 0, but then what? I'm stuck.
Thanks,
J.B.
I need set everything = to 0, but then what? I'm stuck.
Thanks,
J.B.
MathStudent said:Let me make sure I got the equation right
[tex] f(x) = \sqrt[3]{\mid x^2 - 9 \mid - 3} [/tex]
Phew... took me a while but I got the Latex
stunner5000pt said:So
firstly rearrange it to make it look nicer(according to me at least)
[tex] \sqrt[3]{|x^2 - 9|} = 3 [/tex]
try and remove the cube root sign first
then consider teh cases when the |x^2 - 9| is greater than and lesser than or equal to zero
in the first case you simply drop teh absolute values
inthe second case you place a negatie sign in front of the absolute value term and drop the absolute value signs
then solve for x, you should get 4 answers, 2 real answers, and 2 complex (square root of 1, related)
JBauer said:Ok, I have the cube root sign removed and my current equation is:
|x^2 - 9| = 27
although I do not remember how to work out the absolute values from here...
|x^2 - 9| is allways >0stunner5000pt said:so first you'll have |x^2 - 9| > 0, here you should simply keep the whole expression as positive, drop the absolute values and then solve with this equated to 27.
poolwin2001 said:|x^2 - 9| is allways >0
What he may have meant was take cases x^2>=9 and x^2<9
Finding the zeros of a function is important in understanding the behavior of the function and its graph. It helps us identify the points where the function crosses the x-axis and where the output value is equal to zero.
To find the zeros of a function algebraically, set the function equal to zero and solve for the variable. The solutions or roots of the equation will be the zeros of the function.
The location of the zeros of a function can tell us about the symmetry of the graph and the number of times the graph crosses the x-axis. It can also help us determine the maximum and minimum values of the function.
Yes, a function can have multiple zeros or roots. In fact, a polynomial function of degree n can have at most n real zeros.
The terms root and zero are often used interchangeably, but technically a root refers to the solution of an equation while a zero refers to the input value that produces an output of zero for a function.