Can you help me understand how to do this problem. Given the function f(x) = 4(x+3) - 5, solve for the inverse function when x = 3. (1 point)

- anonymous

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- anonymous

To make this easier, let y = f(x). So, we have: \[y = 4(x + 3) - 5\]To solve for the inverse, switch x and y. \[x = 4(y + 3) - 5\]Now, solve for y again in terms for x. Can you take it from there?

- anonymous

3=4y+12 - 5 so 3=4y+7 so -4=4y so y=-1?

- anonymous

Yes! Good job! Also, there's a cool little trick to inverse functions like this. If you're trying to find what the inverse is at an x-value, you can just plug that in for y (or f(x)) in the original and solve for x.

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- anonymous

Can you give me an example? Im not sure I understand that.

- anonymous

what about this when you don't have a value for x and need to do the inverse?
Given the function f(x) = 5x-3/4 , which of the below expressions is correct?
f-1(x) = 3-5x/4
f-1(x) = 4x+3/5
f-1(x) = 4x-3/5
f-1(x) = -5x-3/4

- anonymous

Follow the same steps as in the first example, but this time, since you don't have any values to plug in, leave the x there and solve for y in terms of x. Then, once you get y by itself, replace it with \(f^{-1}(x)\).

- anonymous

So, to get you started, \[f(x) = 5x-\frac34\]\[y=5x-\frac34\]\[x=5y-\frac34\]

- anonymous

it's actually 5x-3 over 4

- anonymous

it wouldn't copy the equation correctly.

- anonymous

Ah ok. No problem. \[f(x) = \frac{5x-3}{4}\]\[y=\frac{5x-3}{4}\]\[x=\frac{5y-3}{4}\]

- anonymous

then how do i do the f-1(x)

- UsukiDoll

split the fractions up
\[x = \frac{5y}{4}- \frac{3}{4}\]

- UsukiDoll

now add 3/4 to both sides.

- anonymous

Well, remember when we let y = f(x)? Solve for y first, then you can just replace the y with the \(f^{-1}(x)\). It's just a notation thing. You can work with f(x) the entire time, it's just a bit messy.

- anonymous

Do you need help with the algebra to solve for y or can you do that part?

- anonymous

can you help?
I got y=3+4X? Is that right?

- UsukiDoll

let me check that for a sec

- anonymous

Not quite. I think you forgot the 5 somewhere.

- UsukiDoll

\[x + \frac{3}{4}= \frac{5y}{4}\]
then divide 5/4 throughout the entire equation .

- anonymous

\[x = \frac{5y - 3}{4}\]\[4x = 5y - 3\]\[5y = 4x + 3\]It looks like you got to here in your algebra. All that's left to do is divide by 5 to get y by itself. Do you get it?

- UsukiDoll

|dw:1439784708621:dw||dw:1439784747500:dw|

- anonymous

I multiplied the entire equation by 4 in the first step, then added 3 on both sides in those first two steps.

- anonymous

okay, i get that!

- UsukiDoll

|dw:1439784792258:dw| it was a good attempt. just that the 5 was missing ^_^

- anonymous

Remember, you're basically doing the opposite of PEMDAS to solve for a variable. Just work backwards!

- UsukiDoll

now the last step is to replace that y with \[f^{-1}(x )\]

- anonymous

okay
thank you!

- anonymous

Yes ^. Like I said before, we let y = f(x) to make it more convenient when writing (It'd take a while to write f(x) and f^-1(x) every time!). So now, you can just replace y with \(f^{-1}(x)\). You can decide to solve it using the f(x), and it'd still be correct, it'd just take longer to write and is a bit more confusing if you're new to algebra. :)

- UsukiDoll

|dw:1439785031869:dw|

- anonymous

Do you know how to explain how to do this?
On the graph of the equation 3x + 2y = 18, what is the value of the y-intercept?

- anonymous

I'm going to sleep in a few minutes, but this last one, sure. A y-intercept is basically where the graph touches the y-axis. What do we know about the x-value at the y-axis?

- anonymous

That's the only information it gives me

- anonymous

and these are the answer choices
-9
-6
6
9

- UsukiDoll

for this equation 3x+2y=18
we need this in y = mx+b form where m is the slope and b i s the y -intercept. You need to rearrange this equation and divide the whole equation by 2

- anonymous

I know, I'm trying to get you through the question without my outright giving you how to do it.

- anonymous

@UsukiDoll I personally think there's a much easier way to do this question, but that works too.

- anonymous

ah okay. Well i put it in y=mx+b format, then I wasn't sure what to do

- anonymous

If you did put it into y = mx + b, then b is your y-intercept by definition.

- anonymous

So the answer would be 9

- anonymous

Yes, it is 9. The point I was trying to make earlier is this. You learned in algebra that the y-intercept is where the graph hits the y-axis, correct?

- anonymous

Yes that makes sense! Thank you for your help! I appreciate it!

- UsukiDoll

2y=-3x+18
y = -3/2x+9
-3/2 <- slope
9<-y-intercept.

- anonymous

At the y-axis, the x-value of all points on the y-axis is 0. In other words, the y-intercept is when x = 0. So, another way to do it (personally faster) is to just let x = 0 and solve for y.
\[3x + 2y = 18\]\[3(0) + 2y = 18\]\[2y = 18\]\[y = 9\]

- anonymous

However, either way works, of course. :)

- UsukiDoll

oh .. that's what you mean by easier way. I never thought of that when I used to to do these problems. for y-intercept, set x = 0 and solve for y XD

- UsukiDoll

I was taught to rearrange to y = mx+b and if there's a number next to y, divide the whole equation by that number. wow tsk tsk. the math professors keeping their good secrets lol

- anonymous

y=mx+b is how I learned, but that makes sense.

- anonymous

lol yeah, lots of ways to think about these types of problems. It's just in the beginning, it's hard to grasp the concept, so you learn rules and directions like (just put into y = mx + b first). However, as you get more used to it, you can start to think about it more and you get little tricks like that.

- anonymous

Anyway, I'm going to sleep. I'm sure if you have anymore questions, others will be glad to help you @gmanmoney .

- anonymous

thanks so much!

- anonymous

Brittany was tracking the increasing temperature in the morning. At 8 a.m. it was 68 degrees Fahrenheit. At 10 a.m. it was 74 degrees Fahrenheit. If Brittany made the function f(x) = 3x + 36, what would the 36 represent? (1 point)
The temperature at midnight
The rate the temperature was increasing
The length of time she recorded for
The total change in degrees

- anonymous

How would I do this one?

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