Question

Find the domain and range of f(x)=4/√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