C3 Help please!

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.

bump

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.

Reply 3

Jamdroid

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).

(edited 8 years ago)

y=10-2lnx-6

Thanks

(edited 8 years ago)

Reply 6

Loola1234

can some1 help me work out 3a

Reply 7

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 :smile:

Reply 8

Loola1234

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 :smile:

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?

Reply 9

Connor_leigh

How do you get rid of the e?

Spoiler

Reply 10

Loola1234

Original post by Connor_leigh

How do you get rid of the e?

Spoiler

what;s a natural log>

Reply 11

Connor_leigh

You normally see it as 'Ln(x)'

Reply 12

Loola1234

Original post by Connor_leigh

You normally see it as 'Ln(x)'

you haven;t been very helpful. bye.

Reply 13

Connor_leigh

I'm not just going to give you the answer. I'm trying to prompt you in the right direction.

Reply 14

Loola1234

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.

Reply 15

davros

Original post by Loola1234

what;s a natural log>

The natural log, usually written ln x or

log_e {x}

, is the inverse function to

e^x

.

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?

Reply 16

Connor_leigh

Original post by davros

The natural log, usually written ln x or

log_e {x}

, is the inverse function to

e^x

This

Reply 17

m8itscharlo

Can someone please help!

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)

Reply 18

Jamdroid

Original post by m8itscharlo

Can someone please help!

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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