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Question

Question: How do you find \(f\left( -4 \right)\) given \(f\left( x \right)=2\)?...

How do you find f(4)f\left( -4 \right) given f(x)=2f\left( x \right)=2?

Explanation

Solution

From the question given it had been asked to find f(4)f\left( -4 \right) and it had been given that f(x)=2f\left( x \right)=2. Now, for example let us consider a function f(x)=af\left( x \right)=a, it tells us that for any value of xx in the given function the answer will be aa that means that we can substitute any value in xx but the answer will be aa.

Complete step by step answer:
Now from the question given we have been asked to find the value of f(4)f\left( -4 \right)
The value of f(4)=2f\left( -4 \right)=2
The f(x)f\left( x \right) is given as a constant function in the question. From the basic concept we know that for constant functions the result will be the same for any value of xx substituted in f(x)f\left( x \right) .
We had been given from the question that f(x)=2f\left( x \right)=2
That means that if we substitute any value in the xx, the answer will remain unchanged.
So, we substitute any value in the given function the answer will be 22
So, if we substitute 4-4 in the given function the answer will be 22
Therefore, f(4)=2f\left( -4 \right)=2

Note:
We should be well aware of the functions and their basic properties. In this type of questions more than using the solving part we have to use the logical part. In this type of question, the answer will be in simply two or three steps if you can get the logic. To get the logic we should know the basic properties of the functions. Similarly in this question we can find the value for any value of xx like f(2)f\left( 2 \right) that would be also 22 .