Question

For the functions u(t)=8t−14 and s(t)=t2−16, what is s(u(3))?

Answer 1

`{ \tt{u(t) = 8t - 14}} \\ { \tt{s(t) = {t}^(2) - 16}} \\ \\ { \tt{s[u(t)] = {(8t - 14)}^(2) - 16}} \\ { \tt{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: s[u(t)]= (64 {t}^(2) - 224t + 196) - 16 }} \\ { \tt{ \: \: \: \: \: s[u(t)] = {64t}^(2) - 224t + 180}}`

So;

`{ \tt{s[u(3)] = 64 {(3)}^(2) - (224 * 3) + 180}} \\ = { \tt{576 - 672 + 180}} \\ = { \tt{84}}`