1. Problem: Find the functions given. 2. For each function, we simply write them as given: - $f(x) = 30$ - $f(x) = 15x + 6$ - $f(t) = 2t^3 - 3t^2 - 4t$ - $S(p) = \sqrt{p} - p$ - $y(x) = \sqrt{x^3 (2 + x)}$ - $y(x) = e^{x+1} + 1$ - $R(a) = (3a + 1)^2$ - $f(v) = \sqrt{v^3} - 2v e^v / v$ - $B(y) = Ay$ 3. Explanation: - For powers and roots, use the rules $\sqrt{x^n} = x^{n/2}$. - For exponential functions, $e^{x+1} = e^x \cdot e^1$. - Simplify expressions carefully, e.g., $\frac{2v e^v}{v} = 2 e^v$ if $v \neq 0$. 4. Simplifications: - $f(v) = \sqrt{v^3} - 2v e^v / v = v^{3/2} - 2 e^v$ 5. Final functions: - $f(x) = 30$ - $f(x) = 15x + 6$ - $f(t) = 2t^3 - 3t^2 - 4t$ - $S(p) = \sqrt{p} - p$ - $y(x) = \sqrt{x^3 (2 + x)}$ - $y(x) = e^{x+1} + 1$ - $R(a) = (3a + 1)^2$ - $f(v) = v^{3/2} - 2 e^v$ - $B(y) = Ay$