(a) To find \(ff(x)\), substitute \(f(x) = 2x^2 + 3\) into itself:

\(ff(x) = f(f(x)) = f(2x^2 + 3) = 2(2x^2 + 3)^2 + 3\).

Expand \((2x^2 + 3)^2\):

\((2x^2 + 3)^2 = 4x^4 + 12x^2 + 9\).

Substitute back:

\(ff(x) = 2(4x^4 + 12x^2 + 9) + 3 = 8x^4 + 24x^2 + 18 + 3 = 8x^4 + 24x^2 + 21\).

(b) Solve \(ff(x) = 34x^2 + 19\):

\(8x^4 + 24x^2 + 21 = 34x^2 + 19\).

Rearrange to form a polynomial equation:

\(8x^4 + 24x^2 + 21 - 34x^2 - 19 = 0\).

Simplify:

\(8x^4 - 10x^2 + 2 = 0\).

Factorize:

\(2(x^2 - 1)(4x^2 - 1) = 0\).

Solve each factor:

\(x^2 - 1 = 0\) gives \(x = 1\).

\(4x^2 - 1 = 0\) gives \(x = \frac{1}{2}\).

Thus, \(x = 1\) or \(x = \frac{1}{2}\).