The following function is one-to-one. Find its inverse. Find the domain and range of f and Please show all of your work.
f(x) = (8+x)/(x)

Question

mathteacher1729 · Answer

How far do go into this problem before getting stuck?

alfie · Answer

$$y = \frac{8+x}{x}$$ The inverse is to find everything in function of x.. so..

$$xy = 8+x \rightarrow xy - x =  8 \rightarrow x(y-1) = 8 \rightarrow x = \frac{8}{y-1}$$

alfie · Answer

Domain, denominator different from zero. So just..

$$x \neq 0$$

anonymous · Answer

alfie- how did you get  this?

alfie · Answer

because your function has just one problem, the denominator. We can't divide by zero, so we have to assure that the denominator must be different from zero. Since you just have "x", you just say "x different from zero".

About the inverse function, as I said, is just about calcs.

anonymous · Answer

ok, so, x $$\neq$$ 0 is the answer?

anonymous · Answer

$$x \neq 0$$

alfie · Answer

$$f \ \ \ \ is \ \ \ \  defined \ \ \ \ \forall x \in \ R \neq 0$$

alfie · Answer

Or if you prefer... (-infinity,0) U (0; + infinity)

anonymous · Answer

ok- is that the complete answer to this equation then? Its asking for the inverse, domain and range.

alfie · Answer

inverse:
$$f(y) = \frac{8}{y-1}$$
Domain:
x ∈ R , x ≠ 0.
Range:
R.

anonymous · Answer

Thank you Alfie! :)