Question

What is the domain and range of the absolute value of the equation \[y = {\text{ }}2x - 1\]?

Answer 1

Hint: Domain and range meaning should be known . Apply it carefully and observe that absolute values only asked to be found in the given question. Absolute values define positive numbers.

Complete step by step answer:
The domain refers to the set of possible input values, and
 The range is the set of possible output values.
For the given function, \[y = \left| {2x - 1\left. {} \right|} \right.\].
where,$y$ is the range which we obtain by giving some values as a domain for $x$.
And here ,absolute values are asked , so only positive answers will come.
we can take real numbers as x .
Hence, the domain for the above function is real numbers.
Coming to range what we will get output when we put the values of domain,
If we apply a real value to the place of x we get a value, which should be only positive as absolute value has been asked to find.
Hence, the range starts from \[0\] to \[\infty \] .
Domain = Real numbers.
Range = \[\left[ {0,\infty } \right)\] .

Note: The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)= $x^2$ is all real numbers, and the domain of \[g\left( x \right) = 1/x\] is all real numbers except for\[x = 0\].
The range of a function is the set of all output values ($y$-values).
The absolute value of a number $x$which is also called modulus of a number $\left| x \right|$ is a non-negative number.