Question

State the domain of function, pa help po pls

Answer 1

Given:

The functions are:

(1) $h(x)=\sqrt{1-x}$

(2) $x+y=4$

(3) $x^2+y^2=16$

To find:

The domain of given functions.

Solution:

Domain is the set of input and x -values.

Value under the square root must be positive because if the number under square root is negative, then it is a complex or imaginary number.

(1) $h(x)=\sqrt{1-x}$

The function is defined if

$1-x\geq 0$

$1\geq x$

The function is defined for all real values of x which are less than or equal to 1.

Therefore, the domain of the function is (-∞,1].

(2) $x+y=4$

It is a linear function and linear function is defined for all real values of x.

Therefore, the domain of the function is (-∞,∞).

(3) $x^2+y^2=16$

It can be written as

$y^2=16-x^2$

$y=\pm \sqrt{16-x^2}$

It is defined if

$16-x^2\geq 0$

$16\geq x^2$

$4\geq x\geq -4$

This function defined for all real values of x from -4 to 4.

Therefore, the domain of the function is [-4,4].