For the function, $f(x)=\left\{\begin{array}{ll}x^{2} & \text { if } x< 2 \\ 4 x-5 & \text { if } x \geq 2\end{array}\right.$, find the following.
(a) $f(5)$
(b) $f(-7)$
(c) $f(2.4)$
(d) $f(-3.2)$

Step 1 ：The function is defined in two parts, one for \(x<2\) and the other for \(x \geq 2\). So, we need to check the value of \(x\) and then apply the corresponding function to find the value of \(f(x)\).

Step 2 ：For \(f(5)\), since \(5 \geq 2\), we use the function \(4x - 5\). Substituting \(x = 5\) gives us \(4*5 - 5 = 15\).

Step 3 ：For \(f(-7)\), since \(-7 < 2\), we use the function \(x^2\). Substituting \(x = -7\) gives us \((-7)^2 = 49\).

Step 4 ：For \(f(2.4)\), since \(2.4 \geq 2\), we use the function \(4x - 5\). Substituting \(x = 2.4\) gives us \(4*2.4 - 5 = 4.6\).

Step 5 ：For \(f(-3.2)\), since \(-3.2 < 2\), we use the function \(x^2\). Substituting \(x = -3.2\) gives us \((-3.2)^2 = 10.24\).

Step 6 ：Final Answer: (a) \(f(5)\) = \(\boxed{15}\) (b) \(f(-7)\) = \(\boxed{49}\) (c) \(f(2.4)\) = \(\boxed{4.6}\) (d) \(f(-3.2)\) = \(\boxed{10.24}\)