Let f and g be differentiable functions of one variable

set $\displaystyle \phi = f(x-t)+g(x+t)$

a) prove that $\displaystyle \phi$ satisfies the wave equation : $\displaystyle \frac{\partial^2 \phi}{\partial t^2} = \frac{\partial^2 \phi}{\partial x^2}$

b) sketch the graph of $\displaystyle \phi$ against $\displaystyle t$ and $\displaystyle x$ if $\displaystyle f(x)=x^2$ and $\displaystyle g(x)=0$

is part a) as simple as ( I can't see it being) $\displaystyle f''(x-t)+g''(x+t)=f''(x-t)+g''(x+t)$