Question

What is the range of the function \[y={{2}^{x-1}}\]?

Answer 1

Hint: For solving this question you should know about calculating the range of the functions. The range of a function is the complete set of all possible resulting values of the dependent variable. And it is calculated if we know the domain of that function.

Complete step by step solution:
We can define the domain of a function as the complete step of possible values of the independent variable. So, we can say that the domain is the set of all possible ‘x’ values which will make the function ‘work’ and will give the output of ‘y’ as a real number. And the range of a function is the complete set of all possible resulting values of the dependent.
According to the question we have to calculate the range of \[y={{2}^{x-1}}\].
If we have to calculate the range of any function flow we can take it as \[f\left( x \right)=y\], and then we have to find the values of x and then we find the values of y with the help of x – values. And we can simplify it by just finding the domain of that function.
And if the equation is given then we can simplify the range by just putting the infinite in that and then we can find the range for the function.
According to our question \[y={{2}^{x-1}}\]
Which is already in simplified form. So, we can determine the range for it by just putting the real value of x and the infinite in it.
If we take any real value of x, then
\[{{2}^{x-1}}>0\]
And if we take \[-\infty \] then,
As \[x\to -\infty ,{{2}^{x-1}}\to 0\] but it will not be equal to zero.
So, the range of the function \[y={{2}^{x-1}}\] is y > 0.

Note: If we find the domain of any function then it will be easy to find the range of that function. So, always first try to find a domain and then calculate the range. And it is important because if the domain is not found then you can’t calculate the range for the same function.