Question

If `g(t) = -3t^3-5t^2` and `h(t) = 2t`, what is `g(h(t))`?

Answer 1

See a solution process below:

Explanation:

To find `g(h(t))` we must substitute `color(red)(h(t))` or `color(red)(2t)` for each occurrence of `color(red)(t)` in `g(t) = -3t^3 - 5t^2`

`g(color(red)(t)) = -3color(red)(t)^3 - 5color(red)(t)^2` becomes:

`g(color(red)(h(t))) = -3color(red)((2t))^3 - 5color(red)((2t))^2`

`g(color(red)(h(t))) = (-3 * color(red)(2)^3 * color(red)(t)^3) - (5 * color(red)(2)^2 * color(red)(t)^2)`

`g(color(red)(h(t))) = (-3 * 8 * t^3) - (5 * 4 * t^2)`

`g(color(red)(h(t))) = 34t^3 - 20t^2`