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1. How would you do these two questions I'm really struggling with the first one and I don't even understand what the second one means.
2. bump
3. (Original post by Loola1234)
bump
For the first one, f^-1(x) is the inverse function, which takes y values and gives you the x value that gives you that y value when you put x into f(x). You should have come across how to find the inverse function given a function.

For the second question, it is tricky to visualise, but keep in mind that 0<a<b and do your standard 'what's the shape of the graph, where are the points where it meets the axes...' etc.
4. (Original post by Loola1234)
How would you do these two questions I'm really struggling with the first one and I don't even understand what the second one means.
Write down y=f(x)
And rearrange the equation so you have x=f(y).
You find the inverse function by simply swapping over Y and X in your new equation.
eg.
F(x) = x+5
Write as y = x+5
Rearrange to isolate x, so x = y-5
Now swap over x and y; so you get y=x-5.
So, F^-1(x) = x-5 in this instance.

The question you've given will require your knowledge of laws of logs, I am sure you can use your notes or text book to find those.

Part b)
Remember the domain of the inverse function is the range of the original (it shouldn't be too important for this question but will help you in many others).

To find the range of the original, draw the graph. Draw your graph of y=e^x and use your graph transformation knowledge to change the graph to fit the equation of F(x). The range of a function is the maximum and/or minimum values y can be.

For the graph y=e^x, there is the asymptote y=0. You'll be able to see the range of this graph is y>0, since there is never a value of y less than or equal to zero.

Part C)
If f(x)= x
Then f(4) = 4

If f(x)= 7x+5
Then f(4) = 7(4)+5 = 33

So just put 4 in replacement of x in the equation f(x) given at the very start of the question.

For ff(x), it means f(f(x)). So replace x with the equation f(x).
Eg.
If f(x) = x+5
ff(x) = f(f(x)) = f(x+5) = (x+5)+5

If f(x) = x^2 - 9x
ff(x) = f(f(x)) = f(x^2+9x) = (x^2+9x)^2 - 9(x^2+9x).
5. y=10-2lnx-6
6. Thanks
7. can some1 help me work out 3a
8. f^-1(x) Is the inverse function of x.
Make the equation y=e^5-x/2+6 And then re arrange to find x.
Then wherever you see a y change it to an x and thats your inverse function .
9. (Original post by Connor_leigh)
f^-1(x) Is the inverse function of x.
Make the equation y=e^5-x/2+6 And then re arrange to find x.
Then wherever you see a y change it to an x and thats your inverse function .
That's the easy part that I can do but the rest is really difficult. I've minused the 6 to get y-6= e^5-x/2
And then what do you do?
10. How do you get rid of the e?
Spoiler:
Show
Take natural logs of both sides
11. (Original post by Connor_leigh)
How do you get rid of the e?
Spoiler:
Show
Take natural logs of both sides
what;s a natural log>
12. You normally see it as 'Ln(x)'
13. (Original post by Connor_leigh)
You normally see it as 'Ln(x)'
you haven;t been very helpful. bye.
14. I'm not just going to give you the answer. I'm trying to prompt you in the right direction.
15. bye.
(Original post by Connor_leigh)
I'm not just going to give you the answer. I'm trying to prompt you in the right direction.
16. (Original post by Loola1234)
what;s a natural log>
The natural log, usually written ln x or , is the inverse function to .

I'm not being funny, but if you haven't come across the natural log you're going to find it difficult to answer questions about inverting functions that involve exponentials. Has your teacher covered this in class, or are you self-teaching?
17. (Original post by davros)
The natural log, usually written ln x or , is the inverse function to .

I'm not being funny, but if you haven't come across the natural log you're going to find it difficult to answer questions about inverting functions that involve exponentials. Has your teacher covered this in class, or are you self-teaching?
This

f(x)= (2x+1)/x
Find ff(x)

The answer is (5x+2)/(2x+1) but the closest I can get is (4x+2)/(2x+1)
19. (Original post by m8itscharlo)

f(x)= (2x+1)/x
Find ff(x)

The answer is (5x+2)/(2x+1) but the closest I can get is (4x+2)/(2x+1)
The only thing wrong is your 4 and their 5. It is very possible your arithmetic is wrong - try looking over what you did and spot the error.
If you can't find it make a new thread including all your working.

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