If f(x) = g(x) then f(x) - g(x) = 0. So we need to define h(x) = f(x) - g(x) and find where h(x) = 0. This is exactly what fzero is made for.
h = @(x) x.^2 - 1 - exp(x/5); % Creates a function handle for your function
Now let's plot and see if we can find a point close to where this function is zero.
x = -2:0.01:2;
plot(x,h(x));
Looks like -1.5 and 1.5 are close.
firstZero = fzero(h,-1.5);
secondZero = fzero(h,1.5);
Now visualize these on the plot:
hold on
plot(firstZero,h(firstZero),'ro');
plot(secondZero,h(secondZero),'ro');
hold off
