Question

let \(f:S\to\mathbb{R}\), \(S\subseteq\mathbb{R}\), and \(P=\mathbb{R^+}\)

determine which of these maps are onto and which ones are one-to-one also describe \(f(P)\)

\(f(x)=2x\): is one-to-one and onto
\(f(P)=P\)

\(f(x)=x-4\): is one-to-one and onto
\(f(P)=\{x\in\mathbb{R}:x>-4\}\)

\(f(x)=x^3\): is one-to-one and onto
\(f(P)=P\)

\(f(x)=x^2+x\): is not one-to-one nor onto
\(f(P)=P\)

\(f(x)=e^x\): is one-to-one but not onto
\(f(P)=\{x\in\mathbb{R}:x>1\}\)

\(f(x)=\tan(x)\): is not one-to-one but is onto
\(f(P)=\mathbb{R}\)\[\]am i right?

Answer 1

I believe you're right.

Answer 2

thx