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Mathematics 41 Online
OpenStudy (oswaldmurphy):

Need help with honors thing for algebra 1. Part 1. Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses. http://prntscr.com/buegvy Part 2. Show your work to prove that the inverse of f(x) is g(x). Part 3. Show your work to evaluate g(f(x)).

OpenStudy (oswaldmurphy):

Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include 5 values for each function. Graph the line y = x on the same graph. Can someone help me and show me how to do this?

OpenStudy (phi):

for part A write \[ y = \frac{x+a}{b}\] to find the inverse, rename y to x and x to y (i.e. "switch x and y") can you do that step ?

OpenStudy (oswaldmurphy):

So part one would = to x = y+a/b?

OpenStudy (oswaldmurphy):

@phi

OpenStudy (phi):

yes but you should use parens x= (y+a)/b to show b is dividing both y and a next step: multiply both sides by b (that means write "b" on both sides) then simplify if you know how.

OpenStudy (oswaldmurphy):

Like that? http://prntscr.com/buespl

OpenStudy (phi):

yes. the b/b on the right side simplifies to 1 x b = y+a we can drop the parens on (y+a) now add -a to both sides and simplify (the right side)

OpenStudy (phi):

you should get xb-a = y or y= b x - a ( x*b it's the same as b*x)

OpenStudy (oswaldmurphy):

Is that part 3?

OpenStudy (phi):

if you compare that to the formula they gave you g(x) = c x - d y = b x - a it looks like we want c to be "b" and d to be "a" g(x) = b x -a f(x) = (x+a)/b those are inverses. they want you to pick numbers for a and b I would pick nice numbers.

OpenStudy (oswaldmurphy):

I am kind of confused :/

OpenStudy (phi):

ok, that means you are missing some idea. did you see how we found y = b x - a using algebra ?

OpenStudy (oswaldmurphy):

Yes. Is that the inverse?

OpenStudy (phi):

yes, we followed a "procedure" to find the inverse: 1) switch x and y 2) solve for y they said that f(x) = (x+a)/b g(x) = c x - d where g(x) is the inverse. we found the inverse was y = b x - a

OpenStudy (oswaldmurphy):

Oh ok. Now replace b and a with, lets say, 1 and 2. So y = 1x - 2, would we do it for the inverse or the inverse and f(x)?

OpenStudy (phi):

for their g(x) = c x - d to match what we found, it must be c is really b and d is "a" so the two pair are f(x) = (x+a)/b g(x) = b x - a

OpenStudy (phi):

Now replace b and a with, lets say, 1 and 2. ok, and using those numbers, you can write down *both* f(x) and g(x)

OpenStudy (phi):

what do you get for f(x) and g(x) using a=2 and b=1 ?

OpenStudy (oswaldmurphy):

f(x) = x + 2 (just removed the /1 :P) g(x) = x - 2

OpenStudy (phi):

now we do part B show f(x) and g(x) are inverses.

OpenStudy (oswaldmurphy):

http://prntscr.com/buf0y0 should my answer look like that for now?

OpenStudy (oswaldmurphy):

I just wrote what we did, is that enough?

OpenStudy (phi):

no. part 2 should be first, and then write: let a=2 and b=2 then write what you have in part 1. all of that is to find f(x) and its inverse. i.e. part A

OpenStudy (oswaldmurphy):

so part 1 is part 2 and part 2 is part 1?

OpenStudy (phi):

now for Part 2. Show your work to prove that the inverse of f(x) is g(x). start with the definitions: f(x) = x + 2 g(x) = x - 2 next, write f( g(x) ) = in the definition of f, everywhere you see x, erase the x, and write in g(x)

OpenStudy (phi):

**so part 1 is part 2 and part 2 is part 1? *** all of that is Part 1. But you wrote it up in the wrong order.

OpenStudy (oswaldmurphy):

Alright, that good? http://prntscr.com/buf4jc

OpenStudy (phi):

yes, but right before f(x)= x+2 you should say g(x) = b x - a and then say: let a=2 and b =1 so that people know how you got f(x)=x+2 and g(x) = x-2

OpenStudy (oswaldmurphy):

Sorry for being such a pane. http://prntscr.com/buf60g

OpenStudy (oswaldmurphy):

Pain, omg my brain is not in the right place today.

OpenStudy (phi):

that looks pretty good. But the last line (for Part 2) were instructions for you to do that to figure out what f( g(x) ) = is equal to. in other words, write f( g(x) ) = write the definition of f(x) here, but replace x with g(x)

OpenStudy (phi):

the definition of f(x) is x+2

OpenStudy (oswaldmurphy):

So, when you say definition do you mean words or what it =? Because that would be f(x-2)

OpenStudy (oswaldmurphy):

OH OK, I GET IT NOW. 1 second.

OpenStudy (oswaldmurphy):

f( g(x) ) = g(x) + 2 ?

OpenStudy (phi):

yes, next, on the right side, replace g(x) with its definition

OpenStudy (oswaldmurphy):

Step 2 still? x - 2 + 2, or just x. So the answer would be f(g(x)) = x?

OpenStudy (phi):

yes, but it's good to show the steps: f( g(x) ) = g(x) + 2 f( g(x) ) = x - 2 + 2 f( g(x) ) = x now we do the same for g( f(x) ) = ??? care to try ?

OpenStudy (oswaldmurphy):

Alright, Part 2 or 3? The answer would be: g(f(x)) = f(x) - 2 g(f(x)) = x + 2 -2 g(f(x)) = x?

OpenStudy (phi):

yes, but (obviously) no ? at the end this is still Part 2 you now say f(g(x)) = x = g(f(x)) which means f(x) and g(x) are inverses.

OpenStudy (phi):

for Part 3, you already did that work in Part 2

OpenStudy (oswaldmurphy):

http://prntscr.com/buffvt

OpenStudy (phi):

yes

OpenStudy (oswaldmurphy):

How do I do part 4 :/

OpenStudy (oswaldmurphy):

Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include 5 values for each function. Graph the line y = x on the same graph.

OpenStudy (phi):

do you have to do it by hand ? you need graph paper

OpenStudy (oswaldmurphy):

I dont have graph paper, and this is an online course... WAT

OpenStudy (phi):

you could use https://www.desmos.com/calculator

OpenStudy (oswaldmurphy):

How would I graph the points?

OpenStudy (phi):

They want a table with 5 points I would use x= -2 , -1 , 0, 1, 2 and figure out f(x) and g(x) for each of those x values

OpenStudy (oswaldmurphy):

Hm, I think I got this one second.

OpenStudy (oswaldmurphy):

http://prntscr.com/bufk46 what would I do next?

OpenStudy (phi):

I would make the first column f(x) and the second g(x) to find the values for f(x) you figure out f(-2), f(-1), etc to, for example, find f(-2), you write the definition of f(x), but replace with x with -2 then simplify.

OpenStudy (phi):

btw, you could make your table in any order, but it makes more sense to order the x's from smallest (-2) to biggest (+2)

OpenStudy (oswaldmurphy):

http://prntscr.com/bufqln @phi

OpenStudy (oswaldmurphy):

So would that make my first point -2, -2?

OpenStudy (phi):

yes, but they want you to "evaluate" f(-2) to get a number for example f(x) = x+2 (that is the definition) f(-2) = -2 + 2 (f(-2) means replace the x with -2) f(-2) = 0 (simplify)

OpenStudy (oswaldmurphy):

http://prntscr.com/bufwoh What would I do next @phi

OpenStudy (oswaldmurphy):

@welshfella Was I supposed to make C b and D a?

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