We say that a function \(f(x)\) is linear in x if we can write \(f(x)\) in the form \(f(x) = ax+b\) for constants \(a\) and \(b\). If a function is not linear, we say that it is nonlinear in x.

Determine if the following functions are linear or nonlinear:

For the function \(f(x) = 5x+3\), \(f(x)\) is linear nonlinear in \(x\).

For the function \(f(x) = \sin (2x+1)\), \(f(x)\) is linear nonlinear in \(x\).

For the function \(f(x) = 2x^2+3\), \(f(x)\) is linear nonlinear in \(x\).

For the function \(f(x) = (2x+1)^2-4x^2\), \(f(x)\) is linear nonlinear in \(x\).

For the function \(f(x) = (\sqrt {x}+1)^2-2\sqrt {x}\), \(f(x)\) is linear nonlinear in \(x\).

For the function \(f(x) = \frac {\sin (x)+5}{3\sin (x)}\), \(f(x)\) is linear nonlinear in \(x\).