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# How would you solve... watch

1. yeah it asks for the exact value at which f(x) = f^-1(x)

f(x) = x^2 - 4, x is less than or equal to 0
f^-1(x) = is the inverse function of f(x)
2. (Original post by haseem)
yeah it asks for the exact value at which f(x) = f^-1(x)

f(x) = x^2 - 4, x is less than or equal to 0
f^-1(x) = is the inverse function of f(x)
I see! You're doing things the hard way (and I don't know why I didn't spot this). It would have saved a lot of bother if you'd put this in your first post!

The graphs of and are reflections of each other in the line . That means that they can only meet on the line , and so the equation you need to solve is (or ) rather than .
3. OMG, I feel so stupid because I wrote that f(x) = x but crossed it out for some stupid reason. But thanks nuodai!
4. I get x = 1/2 (1+sqrt(17)) as one solution, but cannot manage to get the other solution
5. (Original post by haseem)
I get x = 1/2 (1+sqrt(17)) as one solution, but cannot manage to get the other solution
That's wrong I'm afraid. Anyway, there is only one solution because you're given that . This also means that your inverse should actually be , because this must be negative. (It turns out not to make a difference here when calculating the solution, although it does for checking it's correct.)

So proceed as you did before, but take the negative root. Then check that it works.
6. How would you get x = 1/2 (-1-sqrt(13))

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