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functions question

hey there

need some help have my math exam tomorrow:
was doing functions fine until i came across these two sums :s-smilie:

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)!!}}

Reply 1

latentcorpse

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

y=x^2+2x-1

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

x= \sqrt{y+2} - 1

this allows us to write the inverse function down as follows

f^{-1}(x) = \sqrt{x+2}-1

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.