Question

Which of the following are one-to-one functions? (Select all that apply.)
h(x)=IxI+4
d(x)=x^2+7
g(x)=1/(x+1)
f(x)=x^3+4

Please explain your answers too.

Answer 1

one-to-one implies that 1 value in the domain of x maps to exactly one value in the domain of the function of x and vice-versa.

Answer 2

so h(x) for example is NOT a one-to-one function as h(-1) = 5 AND h(1) = 5, which means a 5 in the domain of the function does not map to exactly one point in the domain of x.

Answer 3

its hard to say if 1/x is a function; but that depends on your domain of definition i spose; quads are never one 1-1, and the | | is just a quad in disguise

Answer 4

you should, hopefully, be able to us this information to answer this question now.

Answer 5

Not really

Answer 6

ok - for each function, can you think of a value for x which would give you the same value for the function?
e.g. h(x) gives 5 for x=-1 or x=1
any such function will NOT be a one-to-one function

Answer 7

That one thats cubed cant be it either right?

Answer 8

can you think of two values for x that will give you the same answer for f(x)?

Answer 9

I'm sorry I'm a little confused right now

Answer 10

can you think of two values for x for which the function:\[f(x)=x^{3}+4\]will give you the same answer?

Answer 11

Wait... I think I get what you are saying... since it's an absolute value it will be 1 either way which makes you get 5.

Answer 12

yes - I think you understand now.

Answer 13

Yeah I think I do... Thanks

Answer 14

so which ones do you are one-to-one functions?

Answer 15

g(x)=1/(x+1)
f(x)=x^3+4

Answer 16

perfecto! you are a genius!

Answer 17

lol... Nah