Question

The function f is defined by

Answer 1

\(f:x \rightarrow x^2-x,x \in~\mathbb{R}\)

Answer 2

State whether f is one-to-one,giving a reason for the statement.If the domain of f is restricted to the subset of \(\mathbb{R}\)

Answer 3

for which

Answer 4

\(x\ge~k\)
find the least value of k for which f is one-to-one.

Answer 5

Answer:
No.
f(0)=f(1)=0

Answer 6

Not sure how to do next..

Answer 7

find the least value of k for which f is one-to-one.

Answer 8

I am confused .-.

Answer 9

okay.. xD
r u confused with the question or my answer ?

Answer 10

very confused by the question

and I think the answer might be wrong

Answer 11

nvm
answer is right

Answer 12

-> find where the function is one to one?
there is only one value...

Answer 13

do u hv any hints? ^

Answer 14

is the answer 1/4 ?

Answer 15

hmmm
f(1/4) = (1/4)^2 - (1/4) = 1/16 - 1/4 = 1/16 - 4/16 = -3/16
f(3/4) = (3/4)^2 - (3/4) = 9/16 - 12/16 = -3/16

Answer 16

but close ;)

Answer 17

okay,let me try.. (:

Answer 18

the dot I drew should be the only one-to-one point in this function

Answer 19

excuse my horrible drawing skills x'D

Answer 20

it's okay..it's better than my drawing.. xD

Answer 21

basically, this function is symmetrical
so the one point that is alone without a repeated y value would be the middle point

the repeated points each have their evil twin the same distance from this middle point
you have pointed out that f(0) = f(1)
and so the middle point would be the middle of those two values
do you have a better guess now? ;)

Answer 22

I think i got it

Answer 23

is it x=1/2

Answer 24

mhmm ^_^
thanks what I think your answer should be
although it was really confusing the way they asked it >.>

Answer 25

*that is what I think

Answer 26

i use the completing the square method to find the value based on ur diagram

Answer 27

uhhh
you could have just done
(1 - 0)/2 = 1/2

because you found that f(0) = f(1)
and the middle point should be the perfect middle of those two...

Answer 28

xD

Answer 29

xD

Answer 30

but completing the square works too x'D

Answer 31

it's just more work .-.

Answer 32

Thank you! @Angle ^_^

Answer 33

agree with u @Angle
x'D