if g(t)=4+square root of 9-t, what is the smallest possible value of g(t)
A) 0
B) 3
C) 4
D) 5
E) 9
clearly the smallest value is 4 which is choice C)
why is the smallest value 4?
your equation was
g(t) = 4 + √(9-t)
you already had 4 and you are adding more to it (the √(9-t)), so g(t) can only become larger since by definition the √ of a number yields a positive result.
So when t=9 you would have
g(t) = 4 + 0
= 4
(the smallest value I can ADD to anything is zero)
To find the smallest possible value of g(t), we need to determine where g(t) is minimized.
We can start by analyzing the given function, g(t) = 4 + √(9 - t).
Since the minimum value of the square root function is 0, the smallest possible value of g(t) occurs when the expression inside the square root, (9 - t), is equal to zero.
So, we solve the equation 9 - t = 0 to find the value of t that minimizes g(t).
9 - t = 0
t = 9
Therefore, the smallest possible value of g(t) is obtained when t = 9. Plugging this value into the function:
g(9) = 4 + √(9 - 9) = 4 + √0 = 4 + 0 = 4
So, the correct answer is C) 4.