Functions
\(f\) and \(g\) are two functions such that \((f \circ g)(3)=5\)
What is the value of \((g \circ f)(3)\) ?
If \(f\) is a function with domain \(\mathbb{R}\) and range \(\mathbb{R}\), does there exist a function \(g\) such that \(g(x) = f^{-1}(x)\) ?
In the above image, the red graph is a graph of \(y=f(x)\), for some function \(f\).
What transformation of \(f\) will produce the blue graph in the above graph?
\(f(x)\) is a function with domain \(\mathbb{R}.\)
\(g(x)\) is a horizontal transformation of \(f(x)\) such that \(g(x) = f(x+k).\)
\(h(x)\) is a vertical transformation of \(f(x)\) such that \(h(x) = f(x)+k.\)
If you choose \(f(x)\) carefully, is it possible that \(g(x)\) might equal \(h(x)\) for all \(x\)?
\(f\) is a function whose domain is \(\mathbb{R}\).
\(g\) is a function such that \(g(x)=f^{-1}(x)\)
True or false: The domain of \(g\) must also be \(\mathbb{R}\).