please helpp

if f(x) is 1-1 and if f(x) is never zero can any be said about h(x) = 1/f(x)? is it also 1-1? Give reasons for your answer?

Question

please helpp

if f(x) is 1-1 and if f(x) is never zero can any be said about h(x) = 1/f(x)? is it also 1-1? Give reasons for your answer?

precal · Answer

is that the actual question?  Can you state the question given in your class?  Seems like it is miswritten or something.  What level of math is this?  just curious so I know how to answer it, if I can

anonymous · Answer

its first year calculus and that is what is written in the book

kinggeorge · Answer

I do believe that would also be 1-1. If it were 0, we would run into a problem dividing by 0, but it isn't, and since $f(x)$ takes unique values for unique $x$'s,  $1/f(x)$ must also take unique values.

anonymous · Answer

hmm so just again 1-1 basically means it passes the horizantal and the vertical line test?

kinggeorge · Answer

1-1 means it passes the horizontal line test. However, it must also pass the vertical line test since that's required to be a function.

anonymous · Answer

could we also prove this by defining a 1-1 function saying let us pick two arbitrary points say a,b and h(a) = 1/f(a) and h(b) = 1/f(b)

therefore 1/f(a)=1/f(b) and that implies f(b)=f(a) and that implies b=a and that implies h is a 1-1 function ??

kinggeorge · Answer

You would prove it by saying that: 

Suppose h(a)=1/f(a)=h(b)=1/f(b). Then 1/f(a)=1/f(b) so f(a)=f(b). Since f is 1-1, this implies that a=b. Hence, h is also 1-1.

anonymous · Answer

perfect thanks a lot

anonymous · Answer

could you also help me in this other question please i am going to post please