anonymous
  • anonymous
A student says that the functions f(x) = 2x+2 and g(x) =2x-2 are inverse functions because their graphs are parallel. Is the student's reasoning correct? Justify your answer
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@Nnesha
anonymous
  • anonymous
Please help me @Nnesha
anonymous
  • anonymous
@jim_thompson5910

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anonymous
  • anonymous
Someone please help me....
jim_thompson5910
  • jim_thompson5910
what do you get if you solve y = 2x+2 for x?
anonymous
  • anonymous
Umh, you would get y=x-2/2
anonymous
  • anonymous
Right?
anonymous
  • anonymous
And then the other one would be y=x+2/2
jim_thompson5910
  • jim_thompson5910
yes \[\Large y = \frac{x-2}{2}\] that is equivalent to \[\Large y = \frac{1}{2}x - 1\] what is the slope of the second equation I wrote?
anonymous
  • anonymous
1/2
anonymous
  • anonymous
or would it be -1? Because I know that would be the y intercept right
jim_thompson5910
  • jim_thompson5910
it's 1/2
anonymous
  • anonymous
Ok
jim_thompson5910
  • jim_thompson5910
so in y = 2x+2, the slope is 2 in y = (1/2)x - 1, the slope is 1/2
jim_thompson5910
  • jim_thompson5910
the slopes are not equal, so the lines aren't parallel
anonymous
  • anonymous
And that would mean that the two functions are not inverses, right?
jim_thompson5910
  • jim_thompson5910
no when we solved for x and swapped x and y, we found the inverse
anonymous
  • anonymous
But don't inverse functions have to equal x?
jim_thompson5910
  • jim_thompson5910
I'm just saying that not all inverses are parallel
anonymous
  • anonymous
No i know that, but are they in this scenario?
anonymous
  • anonymous
Are the two equations inverses? I wouldn't think so because they aren't equal to x... Or am I wrong
jim_thompson5910
  • jim_thompson5910
oh you mean y=2x+2 and y=2x-2?
anonymous
  • anonymous
Yeah
jim_thompson5910
  • jim_thompson5910
well you just found the inverse of y = 2x+2 was y = (1/2)x-1 so it is NOT y=2x-2
jim_thompson5910
  • jim_thompson5910
y=2x+2 and y=2x-2 aren't inverses of each other
anonymous
  • anonymous
Oh ok. Yeah, that's what I thought, but I just wanted to make sure. Do you think you could help me with another problem?
anonymous
  • anonymous
Another problem that also has to do with inverse functions...?
jim_thompson5910
  • jim_thompson5910
go ahead
anonymous
  • anonymous
Find the inverse of each function. Then use the definition of inverse functions to verify that the two functions are inverses. 1. f(x) = -3x+3
anonymous
  • anonymous
I know that the inverse for this one is f -1(x)=3-x/3
anonymous
  • anonymous
The other function is g(x)=0.25x+.6
jim_thompson5910
  • jim_thompson5910
use parenthesis and say (3-x)/3
jim_thompson5910
  • jim_thompson5910
keep in mind that 3-x/3 without parenthesis means \(\LARGE 3 - \frac{x}{3}\)
anonymous
  • anonymous
Ok. And the inverse for the second one is f-1(x)=-4(.6-x) right?
anonymous
  • anonymous
Would I have to plug them into each other to see if they are inverses following the definition of inverse functions?
jim_thompson5910
  • jim_thompson5910
y=0.25x+0.6 has the inverse y = 4(x-0.6) or y = 4x-2.4
jim_thompson5910
  • jim_thompson5910
yeah you need to confirm that f(g(x)) = x and g(f(x)) = x
anonymous
  • anonymous
ok, so what would I do next?
anonymous
  • anonymous
Ok. and they are not inverses right?
jim_thompson5910
  • jim_thompson5910
which 2?
anonymous
  • anonymous
there's more than two?
jim_thompson5910
  • jim_thompson5910
I'm lost about what you're asking
anonymous
  • anonymous
You asked me which two
anonymous
  • anonymous
What does that mean?
anonymous
  • anonymous
I apologize. I just don't understand this
jim_thompson5910
  • jim_thompson5910
so you're given 2 functions, right? which 2 functions are you given again?
anonymous
  • anonymous
I don't know
anonymous
  • anonymous
Would it be the two inverses of the functions?
jim_thompson5910
  • jim_thompson5910
f(x) = -3x+3 and g(x)=0.25x+.6 right?
anonymous
  • anonymous
Yes
jim_thompson5910
  • jim_thompson5910
so if you can show that f(g(x)) = x and g(f(x)) = x are both true, then you have proven they are inverses of each other
anonymous
  • anonymous
ok. Thank you for your help.. I'll post another question if I need help.

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