Question

Find the domain. Use interval notation. h(t) = sq rt of 4-3t

Answer 1

Okay so domain in this case are the t values that would be applicable to find a value for h(t)
So we have
[/sqrt(4-3t)/]
And we know that anything under square root should always be greater than or equal to 0 otherwise it will become a complex number!!
So we can write the restrictions as
4-3t>=0
So To solve these kinds of inequalities to directly find the answer we ALWAYS try to write the co-efficient of the variable as 1 and we factorize the expression!
So it can be also written as...
3(4/3-T)>=0
Or
t<=4/3
So now T has to be lesser than or equal to 4/3
So the Domain HAS TO be (-infinity,4/3]
(OBSERVE THE open and closed brackets]
understood the concept behind this? :)

Answer 2

\(4 - 3t \ge 0\)

Subtract 4 from both sides:

\( - 3t \ge -4\)

Divide both sides by -3. Remember to flip the inequality sign since you are dividing by a negative number:

\( \dfrac{- 3t}{-3} \le \dfrac{-4}{-3}\)

\( t \le \dfrac{4}{3}\)

D: \( (-\infty, \frac{4}{3}] \)