Which expressions are equivalent to the one below. Check all that apply. 16^x
2 answers:
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<h2>Answer with explanation:</h2>
Rolle's Theorem states that:
If f is a continuous function in [a,b] and is differentiable in (a,b)
such that f(a)=f(b)
Then there exist a constant c in between a and b i.e. c∈[a,b]
such that: f'(c)=0
Here we have the function f(x) as:
where x∈[-1,3]
- Since the function f(x) is a polynomial function hence it is continuous as well as differentiable over the interval [-1,3].
Also,
f(-1)=15
(Since,
)
and f(3)=15
( Since,
)
- i.e. f(-1)=f(3)
Hence, there will exist a c∈[-1,3] such that f'(c)=0
Hence, the c that satisfy the conclusion is: c=1
Answer:
Step-by-step explanation:
Given function is .
Now let's find it's range.
we know that square root function always gives positive output then:
Hence range of the function is .
we can repeat same process to find the range of all the given choices.
we will find that only 3rd choice has same range.
Hence final answer is