Answer:
The interval of increasing for both the given functions f((x) and g(x) is given by : (-∞, 4)
Step-by-step explanation:
The function f(x) = |3x| + 3
Since, The modulus function is always increasing so adding 3 to it also increase over the whole number line.
So, The interval of increasing for the function f(x) : (-∞, +∞)
The function g(x) = -x² + 8x - 5
⇒ g'(x) = -2x + 8
To find critical points : g'(x) = 0
⇒ -2x + 8 = 0
⇒ x = 4
So, Intervals of increasing or decreasing are : (-∞, 4) and (4, +∞)
Now, On checking g(x) is increasing on (-∞, 4) and decreasing on (4, +∞)
Hence, The interval of increasing for both the given functions f((x) and g(x) is given by : (-∞, 4)
