missashleyn
Someone please help?
Let f(x) = x2 – 16. Find f–1(x).
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missashleyn
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amistre64
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if we solve the problem:
y = x^2 - 16; for x, what does it look like?
amistre64
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and technically, there is no inverse function stated in the choices :/
missashleyn
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I have no idea :(
amistre64
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we need to remember how to manipulate equation around to solve for a particular variable:
y = x^2 - 16
this can be algebrated about to solve for x
missashleyn
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What would I do first?
amistre64
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would you agree that we can subtract 16 from each side to start to get x all alone?
amistre64
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err, add 16 to each side that is
missashleyn
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Yes so it would be y = x^2/16? So C?
amistre64
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y = x^2 - 16
+16 +16
----------------
y+16 = x^2
its not C, I havent gotten to the end results yet .....
amistre64
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do you know how we can get the "^2" off the x?
missashleyn
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Multiply it?
amistre64
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good attempt, but lets try to take the square root, or sqrt it
sqrt(y+16) = sqrt(x^2)
sqrt(y+16) = x
this is the general construct of our inverse function we are looking for, but they like to then swap xs and ys
missashleyn
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Ohhhhh so it's B then?
amistre64
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B seems the most reasonable answer to me :)
missashleyn
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Okay thank you! I have one more like this, could you help me with it too?
amistre64
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i can take a look at it sure
missashleyn
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Let f(x) = 5x + 12. Find f–1(x).
amistre64
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lets try the same process, but this one is simpler since we aint got to sqrt nothing
y = 5x + 12
how do we solve for x so that x is all alone on one side of the equation?
missashleyn
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- 12 from each side
y = 5x + 12
- 12 - 12
y - 12 = 5x
amistre64
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so far so good, now to uncover the x, we should divide off that pesky looking 5 right?
missashleyn
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Yes so..
y - 12 = 5x
----------
5
y - 12/5 = x
missashleyn
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I think I'm confusing myself
amistre64
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you did fine, lets just make sure its looks "proper" :)
\[\frac{y-12}{5}=x\]
missashleyn
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Okay the closest choice I have to that is |dw:1360095933270:dw|
amistre64
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that will work fine ;)
amistre64
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good luck
missashleyn
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Okay awesome, thank you!! :)