can anyone help to solve this?
Let f: R -> R defined as f(x) = 9X2. Determine whether or not the function is one-to-one and onto.
Thanks in Advance
take f(x) = 9, then x = 1 or x = -1.
therefore not 1-1.
for every element in the range, there must be an element in domain..
take -1 in range, does there an element in the domain that will give you -1 when mapped using your function?
A function is said to be one-to-one if , then .
okay, let's take your function as an example.
here, x is either y or -y which contradicts the definition. hence, is not 1-1.
another explanation is that, any value in the range corresponds to a unique value in the domain..
A function is said to be onto Y if the range of f is Y.
in your function, defined by , the range is and not R, therefore, f is not onto R.
here, it says that for all the values in the range must corresponds to a value in the domain.