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

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- jamiebookeater

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- anonymous

- anonymous

Please help me @Nnesha

- anonymous

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## More answers

- anonymous

Someone please help me....

- jim_thompson5910

what do you get if you solve y = 2x+2 for x?

- anonymous

Umh, you would get y=x-2/2

- anonymous

Right?

- anonymous

And then the other one would be y=x+2/2

- 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

1/2

- anonymous

or would it be -1? Because I know that would be the y intercept right

- jim_thompson5910

it's 1/2

- anonymous

Ok

- jim_thompson5910

so in y = 2x+2, the slope is 2
in y = (1/2)x - 1, the slope is 1/2

- jim_thompson5910

the slopes are not equal, so the lines aren't parallel

- anonymous

And that would mean that the two functions are not inverses, right?

- jim_thompson5910

no when we solved for x and swapped x and y, we found the inverse

- anonymous

But don't inverse functions have to equal x?

- jim_thompson5910

I'm just saying that not all inverses are parallel

- anonymous

No i know that, but are they in this scenario?

- anonymous

Are the two equations inverses? I wouldn't think so because they aren't equal to x... Or am I wrong

- jim_thompson5910

oh you mean y=2x+2 and y=2x-2?

- anonymous

Yeah

- 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

y=2x+2 and y=2x-2 aren't inverses of each other

- 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

Another problem that also has to do with inverse functions...?

- jim_thompson5910

go ahead

- 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

I know that the inverse for this one is f -1(x)=3-x/3

- anonymous

The other function is g(x)=0.25x+.6

- jim_thompson5910

use parenthesis and say (3-x)/3

- jim_thompson5910

keep in mind that 3-x/3 without parenthesis means \(\LARGE 3 - \frac{x}{3}\)

- anonymous

Ok. And the inverse for the second one is f-1(x)=-4(.6-x) right?

- anonymous

Would I have to plug them into each other to see if they are inverses following the definition of inverse functions?

- jim_thompson5910

y=0.25x+0.6 has the inverse y = 4(x-0.6) or y = 4x-2.4

- jim_thompson5910

yeah you need to confirm that f(g(x)) = x and g(f(x)) = x

- anonymous

ok, so what would I do next?

- anonymous

Ok. and they are not inverses right?

- jim_thompson5910

which 2?

- anonymous

there's more than two?

- jim_thompson5910

I'm lost about what you're asking

- anonymous

You asked me which two

- anonymous

What does that mean?

- anonymous

I apologize. I just don't understand this

- jim_thompson5910

so you're given 2 functions, right? which 2 functions are you given again?

- anonymous

I don't know

- anonymous

Would it be the two inverses of the functions?

- jim_thompson5910

f(x) = -3x+3 and g(x)=0.25x+.6 right?

- anonymous

Yes

- 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

ok. Thank you for your help.. I'll post another question if I need help.

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