1) f(x)=3x+1 g(x)=x^2+5x Find f(g(-6))

To find \( f(g(-6)) \), we need to first evaluate \( g(-6) \) and then use that result as the input for the function \( f(x) \).<br /><br />1. Evaluate \( g(-6) \):<br />\[ g(x) = x^2 + 5x \]<br />\[ g(-6) = (-6)^2 + 5(-6) \]<br />\[ g(-6) = 36 - 30 \]<br />\[ g(-6) = 6 \]<br /><br />2. Now, use the result from \( g(-6) \) as the input for \( f(x) \):<br />\[ f(x) = 3x + 1 \]<br />\[ f(g(-6)) = f(6) \]<br />\[ f(6) = 3(6) + 1 \]<br />\[ f(6) = 18 + 1 \]<br />\[ f(6) = 19 \]<br /><br />Therefore, \( f(g(-6)) = 19 \).