a function f has its domain (−1, 3) and range (−4, 6).
Find the domain and range of a function g(x) = f( √ x) if possible.
Your attached image is small. Next time, take two or three pictures instead of one. That way, each image will post larger.
Your function f(x) = 5/8x^2 + 5/4x - 27/8
The domain of this function is all Real numbers.
The range of this function is all Real numbers larger than or equal to -4.
However, if we restrict x to values between -1 and 3, then the corresponding y values lie between -4 and 6. In other words, the
restricted domain and range for your function match what's stated in the exercise.
There are many other functions with restricted domain and range that match. Here's two more:
f(x) = 5/2x^2 - 5x - 3/2
f(x) = 3/2x^3 - 25/6x^2 + 1/3x + 2
Function g is a composite function:
g(x) = f(sqrt(x))
What is the smallest value of x for which we can take the square root?
In addition to the restricted domain for f, are there any other restrictions on how large x can be?
Give an example of a function f(x) that is not increasing and decreasing and satisfies the domain and range.
I do not understand this.
First, it seems like the wording ought to be "not increasing
or decreasing" because it has to be one or the other, not both at once.
Second, a function that is neither increasing nor decreasing is a constant function. No constant function has a range of (-4,6).
