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Urgent help with OCR June 2005 C3 Q9 iii

really really stuck on this one and desperatly need help because i even cheated and got the mark scheme to see if i could understand it after seeing the answer and i still cant work out how to even start doing it.

function f is defied by f(x)=sqrt(mx+7)-4, where x >= -7/m and m is a positive constant.

ive worked out the inverse function to be = ((x+4)^2-7)/m
and it is given that the function and its inverse do not meet. explain how it can be deduced that neither cureve meets the ine y=x and hence determine the set of possible values of m.

any help is greatly appreciated coz im at a loss.
quinnie2203
explain how it can be deduced that neither cureve meets the ine y=x


It's important to note that the inverse of a function is a reflection in the line y=x of the original. Hence, if the function and it's inverse don't meet, they cannot meet the line y=x either.

quinnie2203
hence determine the set of possible values of m


Rearrange either the equation for the function or the inverse, into the form for quadratic equations (you will get coefficients of x^2 and x in terms of m, not just constants), then use the discriminant, b^2-4ac and factorise to find the range.

Hope this helps.
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quinnie2203
OP
2
thanx this is wat ive beein trying to, but i canno work out. wat is the actual equation im rearranging, ive tried x=f(x), x=f^-1(x), -7/m=f(x) and -7/m=f^-1(x) and i get a quadratic for x in terms of m, but using the discriminant just gets m^2 + a constant. usually 23. can anyone help out or post a solution. thanks
quinnie2203
thanx this is wat ive beein trying to, but i canno work out. wat is the actual equation im rearranging, ive tried x=f(x), x=f^-1(x), -7/m=f(x) and -7/m=f^-1(x) and i get a quadratic for x in terms of m, but using the discriminant just gets m^2 + a constant. usually 23. can anyone help out or post a solution. thanks

Use f(x)=xf(x)=x or f−1(x)=xf^{-1}(x)=x. Your discriminant (simplified) should be m2−16m+28m^2-16m+28. See if you can get that, then factorise it, and hence state the values of m.
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CamFam
I still don't understand this question, please can someone help me
Reply 5
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fhlux
6
bump
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Notnek
21
Original post by fhlux
bump

Please start a new thread if you need help. This one is nearly 10 years old!

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