Need Help on Pre Cal

This is a piecewise function. It's composed of 3 pieces of other functions. A piecewise function is a function that changes its identity based on what the input is.

We have three different situations here

If t = 17, then h(t) = sqrt(17t) based on what the first row says
If t = 19, then h(t) = -34/t which is the second row of the piecewise function.
If t does not equal either 17 or 19 (ie t is anything but those values), then h(t) = 23-t

The notation h(17) means we want to evaluate h(t) when t = 17. So we'll use the first case mentioned above. Plug t = 17 into h(t) = sqrt(17t) to get...

h(t) = sqrt(17t)

h(17) = sqrt(17*17)

h(17) = sqrt(17^2)

h(17) = 17

In the last step, I used the rule that sqrt(x^2) = x when x is nonnegative.