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C3 functions question

for part (b) I don't understand why f^-1(x)= -root(3x+4) is the answer but (+)root(3x+4) is wrong

and for part (civ) I don't know how they have got to -root(6) and -2, I got the -root6 but I don't know if I've done it right if I only got one answer
Original post by mica-lwe
for part (b) I don't understand why f^-1(x)= -root(3x+4) is the answer but (+)root(3x+4) is wrong

and for part (civ) I don't know how they have got to -root(6) and -2, I got the -root6 but I don't know if I've done it right if I only got one answer


For (b) the clue is in the question somewhere.

For (civ) think about the modulus signs. This is sneakily linked to your query in (b) too.
(edited 8 years ago)
Original post by mica-lwe
for part (b) I don't understand why f^-1(x)= -root(3x+4) is the answer but (+)root(3x+4) is wrong

and for part (civ) I don't know how they have got to -root(6) and -2, I got the -root6 but I don't know if I've done it right if I only got one answer


Could I ask what paper this is from? So I can check my answers.
Reply 4
Original post by SeanFM
For (b) the clue is in the question somewhere.

For (civ) think about the modulus signs. This is sneakily linked to your query in (b) too.


I get it now, forgot to do the -ve of the equation as well as the positive

with part (b) I'm still not sure how to get the answer without drawing the graphs on my calculator, even that didn't make it clear for me...
Reply 5
Original post by randlemcmurphy
Could I ask what paper this is from? So I can check my answers.


Jan'13
Original post by mica-lwe
Jan'13


Thanks.
Original post by mica-lwe
I get it now, forgot to do the -ve of the equation as well as the positive

with part (b) I'm still not sure how to get the answer without drawing the graphs on my calculator, even that didn't make it clear for me...


The clue is after it says 5 and before it says (a).
Reply 8
Original post by SeanFM
The clue is after it says 5 and before it says (a).


because it's </= 0?
Original post by mica-lwe
because it's </= 0?


Well done :smile:

Do you see why you've got the answer to (b) now?
Reply 10
Original post by SeanFM
Well done :smile:

Do you see why you've got the answer to (b) now?


Yeah I think so, will it tell me which is the right answer in the exam if i just put some values for x into it?
Original post by mica-lwe
Yeah I think so, will it tell me which is the right answer in the exam if i just put some values for x into it?


Yes. If a function takes x and outputs y, then putting y in to the inverse function should give you x.
If you have to find the inverse your domain and range of the original function swap around. So in the case of this question, you got a (+/-)sqrt(3x+4),

you set 3x+4 >(or equal to) 0
3x >(or equal to) -4
x >(or equal to) -4/3


which is the same as the range on your original function. Since the domain on your original function is less than or equal to 0, the range of your inverse must be less than or equal to 0, which I think explains the negative sign (any value obtained from subbing in x values will be less than 0 or equal to it).


If you don't know what to do, I am assuming you get access to a graphical calculator in your exam - just remember the real inverse function will be a reflection in the line y=x. So if you draw all the graphs, the one which reflects the original f(x) function in y=x will be the correct inverse.
(edited 8 years ago)

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