We know that, as per a corollary of intermediate value theorem, if a function f(x) is continuous on a closed interval [a,b], and values of f(a) and f(b) have opposite signs, then the function f(x) is guaranteed to have a zero on the interval (a,b).
So, basically, we need to figure out two values of x, at which the values of the given cubic function have opposite signs.
Let us consider the interval [-2,1].
We have . Upon substituting the values x=-2 and x=1 one by one, we get:
We can see that signs of values of the function at x=-2 and x=1 are opposite, therefore, as per intermediate value theorem, the function is guaranteed to have a zero on the interval [-2,1]
Using logarithmic function concepts, it is found that the correct statement is:
x = 9 is a true solution and x = -9 is an extraneous solution.
<h3>What is a logarithmic function?</h3>
A logarithmic function is modeled by:
It means that:
In this problem, we have that:
Applying the power property:
Applying the definition:
As the logarithm function is defined only for positive values, the correct statement is:
x = 9 is a true solution and x = -9 is an extraneous solution.
You can learn more about logarithmic function concepts at brainly.com/question/26302013
Answer:
Step-by-step explanation:
17 x 0.75 =12.75
12.75 + 1.25= 14
You have to isolate the variable in order to solve this inequality, and whatever we do to one side has to be done to the other.
Since the 1 on the left side is negative, you have to add 1 to both sides to get rid of it
-1 + 1 = 0
4 + 1 = 5
The final answer would be r>5