I've got a test on Monday and I have to get these off my back, thanks

**Graphs**

*Find algebraically the implied domain of $\displaystyle \frac{1}{\sqrt{4x-x^2}}$. (3 marks)*

7 lines to write your answer! Wut? I don't have a concrete method of doing this either... since are Not supposed to use calculus . But we are of course allowed limits. Besides... I've never seen this function before... we never studied it in class. I'd be happy if someone could also find the range, just so if another question asks about that then I'm prepared.

*The rule for the inverse function of*

*$\displaystyle f:[1,\infty) \rightarrow R, f(x)=(x-1)^2+4$ is:*

*A $\displaystyle f^{-1}(x)=1+\sqrt{x-2}$*

*B $\displaystyle f^{-1}(x)=1-\sqrt{4-x}$*

*C $\displaystyle f^{-1}(x)=1+\sqrt{x-4}$*

*D $\displaystyle f^{-1}(x)=1-\sqrt{x-4}$*

*E $\displaystyle f^{-1}(x)=1+\sqrt{4-x}$*

Hmm? I thought it wouldn't have an inverse function because of the plus-minus roots.

**Probability**

*Bill, Bob, and Ben fire one shot at a target.*

*The probability that Bill hits the target is $\displaystyle \frac{4}{5}$*

*The probability that Bob hits the target is $\displaystyle \frac{3}{4}$*

*The probability that Ben hits the target is $\displaystyle \frac{2}{3}$*

*i) Find the probability that only Ben's shot hits the target. (2 marks)*

*ii) given that only one shot hits the target, it is the shot from Ben. (6 marks)*

(What's the difference between these two questions??)

*Ben enters a competition firing 3 shots at the same target. The probability*

*he hits the target remains constant at $\displaystyle \frac{2}{3}$. **Given that he hits the target at least once, what is the probability that he hits it*

*exactly twice? (4 marks)*