Question

Find the domain and range of the function

1.

`f(x) = (2)/(3x - 1)`
2.

`g(x) = \sqrt{16 - {x}^(4) }`

Answer 1

#2: This function is not defined if the denominator = 0. So, steal the denom. and set it = to 0, and then solve the resulting eqn: 3x-1=0, 3x = 1, x = 1/3.
The domain is the set of all real numbers except for x = 1/3. The range is the set of all real numbers except for y = 0.

#4: this function will not be defined if 16-x^4 is less than 0.
so you must solve the inequality x^4 ≤ 16. Take the 4th root of both sides. The domain is (-2, 2). By all means, check. Suppose x = 1.5. is x^4≤16?

The smallest value y can have is zero, which occurs when x = plus or minus 2.