4. State the Domain and Range of the following: a) $f(x)=2(x-1)^{\wedge} 2-4$ b) $f(x)=5(x+1)^{\wedge} 2+1$

Step 1 ：Given functions: \(f(x)=2(x-1)^2-4\) and \(f(x)=5(x+1)^2+1\)

Step 2 ：Both functions are quadratic functions in the form of \(f(x)=a(x-h)^2+k\)

Step 3 ：The domain of a quadratic function is all real numbers

Step 4 ：To find the range, determine if the parabola opens upwards or downwards and find the vertex

Step 5 ：For \(f(x)=2(x-1)^2-4\), the parabola opens upwards and the vertex is \((1, -4)\)

Step 6 ：For \(f(x)=5(x+1)^2+1\), the parabola opens upwards and the vertex is \((-1, 1)\)

Step 7 ：Final Answer: \(\boxed{\text{a) Domain: }(-\infty, \infty), \text{ Range: }[-4, \infty)}\)

Step 8 ：Final Answer: \(\boxed{\text{b) Domain: }(-\infty, \infty), \text{ Range: }[1, \infty)}\)