What is the range of this function

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ihollarmide

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FInd the range of the function [MATH]f\left(x\right)\:=\:a\:+bcos\left(x\right)\:for\:0\:\le \:x\:\le 2\pi [/MATH] given that [MATH]f\left(0\right)\:=\:10\:and\:f\left(\frac{2}{3}\pi \right)\:=\:1[/MATH]. I was able to get the value of a to be 4 and b = 6.
 
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ihollarmide said:
FInd the range of the function [MATH]f\left(x\right)\:=\:a\:+bcos\left(x\right)\:for\:0\:\le \:x\:\le 2\pi [/MATH]
Click to expand...
What is the maximum value of the function f(x) within the given domain?​
​
What is the minimum value of the function f(x) within the given domain?​

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.
 
Subhotosh Khan said:
What is the maximum value of the function f(x) within the given domain?​
​
What is the minimum value of the function f(x) within the given domain?​

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.
Click to expand...
I have edited the question to include what I have been able to do. Thanks
 
Either your a and b are wrong, or you copied the problem wrong. Should that second 10 have been a 1?

To finish the problem, think about what the largest and smallest value of the cosine are.
 
Subhotosh Khan said:
What is the maximum value of the function f(x) within the given domain?

What is the minimum value of the function f(x) within the given domain?
Click to expand...

Using the value of a = 4 and b = 6. I was able to get f(x) to be 10 when x = 0 and f(x) to be also 10 when x is 2pi
 
ihollarmide said:
Using the value of a = 4 and b = 6. I was able to get f(x) to be 10 when x = 0 and f(x) to be also 10 when x is 2pi
Click to expand...
What is the value of f(x) when x = π/2?

What is the value of f(x) when x = π?

What is the value of f(x) when x = 3π/2?

What is the maximum value of the function f(x) within the given domain?

What is the minimum value of the function f(x) within the given domain?
 
Subhotosh Khan said:
What is the value of f(x) when x = π/2?

What is the value of f(x) when x = π?

What is the value of f(x) when x = 3π/2?

What is the maximum value of the function f(x) within the given domain?

What is the minimum value of the function f(x) within the given domain?
Click to expand...
Using f(x) = a + bcos(x). a = 4, b =6. Therefore f(x) = 4 + 6cos(x).
Hence;
f(x) when x = π/2 is 1.
f(x) when x = π is is -2.
f(x) when x = 3π/2 is 4.

I don't understand what you mean by the given domain. Bu if you mean this: 0≤x≤2π. Then I take it that the minimum is 0 and the maximum is 2π. In that case:
Minimum value, f(x) when x = 0 is 10.
Maximum value, f(x) when x = 2π is 10.
 
ihollarmide said:
Using f(x) = a + bcos(x). a = 4, b =6. Therefore f(x) = 4 + 6cos(x).
Hence;
f(x) when x = π/2 is 1...................................................Incorrect
f(x) when x = π/2 is 4
f(x) when x = π is is -2.
f(x) when x = 3π/2 is 4.

I don't understand what you mean by the given domain. Bu if you mean this: 0≤x≤2π. Then I take it that the minimum is 0 and the maximum is 2π. In that case:
Minimum value, f(x) when x = 0 is 10.
Maximum value, f(x) when x = 2π is 10.
Click to expand...
Your original quest is:

Find the range of the function f(x).......

Please lookup the definition of the range of a function ........ and tell us what you found.
 
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