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# functions question Watch

1. hey there
need some help have my math exam tomorrow:
was doing functions fine until i came across these two sums
1. If f(x)=2x+3 and g(f(x))=x find g(x)

2. f(x)=x^2 + 2x - 1 solve the equation f^-1(x)=4 {{i know how to do the solving part but i just cant get f^-1(x)!!}}
2. ok. well if f takes x to 2x+3 and g(f(x))=x then g takes 2x+3 back to x i.e. g is the inverse of f - this should be fairly easy to work out.

for the 2nd one, it is a bit more complicated.
if we write

we want to write x in terms of y in order to find the inverse function.
you should complete the square and rearrange to find

this allows us to write the inverse function down as follows

then you should be able to plug in various values for x.
Note that you will need to do all the completing the square stuff in the middle even though i gave you the final answer.

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Updated: November 28, 2010
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