Find the domain of the function. f(x)=x+4−1−xx

Question

Find the domain of the function.  f(x)=x+4−1−xx

Isma Jimenez · Accepted Answer

Step 1
The domain is a set of x-values where the function is defined. In other words, the domain is the interval of x-values in which the graph of the function is defined.
We have to find the domain of

f (x) = \sqrt{x + 4} - \frac{\sqrt{1 - x}}{x}

S. Since we know that function is not defined if its denominator becomes 0. Here, x os in denominator. Therefore, x should not be 0. i. e.

x \neq 0

Step 2
We know that in square root, the value must not be negative. i.e. the values should be greater than or equal to 0. Here, we have two square root expressions

\sqrt{x + 4}

and

\sqrt{1 - x}

. To defined

f (x), x + 4 \geq 0

and

1 - x \geq 0

. Solve both the inequalities.

x + 4 \geq 0

x \geq - 4

...(1)

1 - x \geq 0

x - 1 \leq 0

x \leq 1

...(2)
From the inequalities (1) and (2),

- 4 \leq x \leq 1

. But

x \neq 0

. So we have to remove

x = 0

value from

- 4 \leq x \leq 1

. Hence, the domain of f(x) is

[- 4, 0) \cup (0, 1]

.

Find the domain of the function. f(x)=\sqrt{x+4}-\frac{\sqrt{1-x}}{x}

Answered question

Answer & Explanation

New Questions in Pre-Algebra