1) d) Yes as the function is one-to-one
e) For inverse, swap x and y, therefore;
)
 + 2)
2) Maybe I'm missing something but, yes? IIRC, a function may have to be to one-to-one so this may be incorrect, not sure.
3) Same as 2... yes?
d) Either solve the inverse to equal the original or solve either (the original or the inverse) to equal x (as they are symmetrical about the line y=x if they intersect it must be on this line)
6) a) No as
)
is not a one-to-one function
b) You need to restrict the domain such that the function will be one-to-one. As the turning point is at 2, the maximal domain such that the function will be one-to-one will be either
or
)
*Note the inverse function will exist if for the domain
the second value is < 2 and for the domain
the left value is > 2 (those two are just the largest possible)
- Yes
)
refers to the inversion function of
. The inverse function of
 = x^{2})
will only exist if the domain is restricted to make it one-to-one. For example if the domain of
was
)
then the inverse function would be
 = \sqrt{x})
. But if the domain of
was
the the inverse function would be
 = -\sqrt{x})
as range
= domain
)
.
- You restrict the domain of
such that
is a one-to-one function so that
will exist
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