Solve h(x) = { x<3: 2/(x-1), x ≥ 3: (2/3)x - 4 }

Evaluate

h (x) = x < 3 \div \frac{2}{x - 1}, x \geq 3 \div (\frac{2}{3} x) - 4

Separate the function into parts to determine the domain of each part

3 \div ((\frac{2}{3}) x) - 4 3 \div ((\frac{2}{3}) x) 3 \div \frac{2}{x - 1} \frac{2}{x - 1} x - 1

The domain of a polynomial function is the set of all real numbers

x \in R 3 \div ((\frac{2}{3}) x) 3 \div \frac{2}{x - 1} \frac{2}{x - 1} x - 1

The domain of a rational function are all values of x for which the denominator is not equal to 0

More Steps

x \in R x \neq = 0 3 \div \frac{2}{x - 1} \frac{2}{x - 1} x - 1

The domain of a rational function are all values of x for which the denominator is not equal to 0

More Steps

x \in R x \neq = 0 x \in R \frac{2}{x - 1} x - 1

The domain of a rational function are all values of x for which the denominator is not equal to 0

More Steps

x \in R x \neq = 0 x \in R x \neq = 1 x - 1

The domain of a polynomial function is the set of all real numbers

x \in R x \neq = 0 x \in R x \neq = 1 x \in R

Solution

x \in (- \infty, 0) \cup (0, 1) \cup (1, + \infty)

Function