Question

Wise Defined Functions The function f is defined as follows. f(x)={(-3x+5 if x<1),(4x-2 if x>=1):}

Find the domain of the function.

Answer 1

The domain of the function f(x) is all real numbers since there are no restrictions on x in either piece of the function.

Step-by-step explanation:

The domain of a function consists of all the possible input values (x-values) that the function can accept. For the piecewise-defined function f(x), we have two conditions:

• For x < 1, f(x) = -3x + 5.
• For x ≥ 1, f(x) = 4x - 2.

Since there are no further restrictions given for x in either piece of the function, the domain of f(x) is all real numbers, because it can take any real number as input. Mathematically, this is expressed as (-∞, ∞) or 'all real numbers.'