Examine the function f(x)=x+(3/x). Find the point on the curve at which the tangent lines pass through the point (1, 1).
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<h2>Hello!</h2>
The answer is:
The range of the function is:
Range: y>2
or
Range: (2,∞+)
<h2>Why?</h2>To calculate the range of the following function (exponential function) we need to perform the following steps:
First: Find the value of "x"
So, finding "x" we have:
Second: Interpret the restriction of the function:
Since we are working with logarithms, we know that the only restriction that we found is that the logarithmic functions exist only from 0 to the possitive infinite without considering the number 1.
So, we can see that if the variable "x" is a real number, "y" must be greater than 2 because if it's equal to 2 the expression inside the logarithm will tend to 0, and since the logarithm of 0 does not exist in the real numbers, the variable "x" would not be equal to a real number.
Hence, the range of the function is:
Range: y>2
or
Range: (2,∞+)
Note: I have attached a picture (the graph of the function) for better understanding.
Have a nice day!