Question

find the domain and range of f(x) = 4/root(8-x)​

Answer 1

Answer:

Domain={x:1<=x<8,x belongs to real numbers}

Range={all real numbers except zero}

Step-by-step explanation:

f(x)=4/(8-x)^1/2

so there are two conditions for x

1. x can't be zero as it is in the denominator and if there is zero in the denominator then the value is undefined.

2. x can't be negative as there is a square root and if there is a negative no. with a square root then it will be a complex number with no possible value.

By taking both the points into consideration we arrive a t the conclusion that domain of x should be all positive real numbers ranging from 1 to 7

for finding range we can substitute y in place of f(x)

and use y as a variable and x as a function

y=4/(8-x)^1/2

8-x=4/y^2

8-4/y^2=x

(8y^2 -4)/y^2=x

Here we have only one condition for y that is the denominator shouldn't be zero so we can say that the range should be all real values except zero

Answer 2

Given: f(x) = 4/root(8-x)​  

To find: The domain and range of f(x).

Solution:

In the given function, the set of values that can be substituted in place of x such that the value of the function is well defined is called the domain of the function. The set of values of the function for every value in the domain is called the range of the function.

The x in the function cannot be replaced by 8 or a number greater than 8. If x is replaced by 8, the denominator becomes zero and hence, the function is undefined. If x is replaced by a number greater than 8, then the denominator becomes the square root of a negative number which again makes the function undefined. Hence, the domain of the function is written as

(-∞, 8)

The range of the function keeps decreasing as the value of x decreases. Hence, the range of the function is

(-∞, 4]

Therefore, the domain and range of f(x) is (-∞, 8) and (-∞, 4], respectively.