Question

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

Answer 1

@Nnesha

Answer 2

Please help me @Nnesha

Answer 3

@jim_thompson5910

Answer 4

Someone please help me....

Answer 5

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

Answer 6

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

Answer 7

Right?

Answer 8

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

Answer 9

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?

Answer 10

1/2

Answer 11

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

Answer 12

it's 1/2

Answer 13

Ok

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

But don't inverse functions have to equal x?

Answer 19

I'm just saying that not all inverses are parallel

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

Yeah

Answer 24

well you just found the inverse of y = 2x+2 was y = (1/2)x-1
so it is NOT y=2x-2

Answer 25

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

Answer 26

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?

Answer 27

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

Answer 28

go ahead

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

use parenthesis and say (3-x)/3

Answer 33

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

Answer 34

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

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

ok, so what would I do next?

Answer 39

Ok. and they are not inverses right?

Answer 40

which 2?

Answer 41

there's more than two?

Answer 42

I'm lost about what you're asking

Answer 43

You asked me which two

Answer 44

What does that mean?

Answer 45

I apologize. I just don't understand this

Answer 46

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

Answer 47

I don't know

Answer 48

Would it be the two inverses of the functions?

Answer 49

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

Answer 50

Yes

Answer 51

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

Answer 52

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