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)

Question

anonymous · Answer

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 · Answer

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

anonymous · Answer

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.

anonymous · Answer

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

anonymous · Answer

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 · Answer

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 · Answer

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

anonymous · Answer

it's actually 5x-3 over 4

anonymous · Answer

it wouldn't copy the equation correctly.

anonymous · Answer

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

anonymous · Answer

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

usukidoll · Answer

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

usukidoll · Answer

now add 3/4 to both sides.

anonymous · Answer

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 · Answer

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

anonymous · Answer

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

usukidoll · Answer

let me check that for a sec

anonymous · Answer

Not quite. I think you forgot the 5 somewhere.

usukidoll · Answer

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

anonymous · Answer

$$x = \frac{5y - 3}{4}$$$$4x = 5y - 3$$$$5y = 4x + 3$$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 · Answer

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