2) g(t)=-2t-1 h(t)=t^3-t Find g(h(-2))

To find \( g(h(-2)) \), we need to follow these steps:<br /><br />1. Evaluate \( h(-2) \).<br />2. Use the result from step 1 as the input for \( g(t) \).<br /><br />First, let's evaluate \( h(-2) \):<br /><br />\[ h(t) = t^3 - t \]<br /><br />So,<br /><br />\[ h(-2) = (-2)^3 - (-2) \]<br />\[ h(-2) = -8 + 2 \]<br />\[ h(-2) = -6 \]<br /><br />Next, we use this result as the input for \( g(t) \):<br /><br />\[ g(t) = -2t - 1 \]<br /><br />So,<br /><br />\[ g(h(-2)) = g(-6) \]<br />\[ g(-6) = -2(-6) - 1 \]<br />\[ g(-6) = 12 - 1 \]<br />\[ g(-6) = 11 \]<br /><br />Therefore, \( g(h(-2)) = 11 \).