Find the domain and range of the function

Question

y=f(x)=1/sqrt(x-36).?

Answer 1

Domain :

The domain is all values that x can be take on( all x values except which make the function undefined )

Given function :f(x)=1/sqrt(x-36)

The function f(x) is undefined when denominator = 0.

So √(x-36)=0

x-36=0

x=36

Actually x = 36 is domain for x-36.

additionally we have square root(√).So all value below 36 are gives negative result for x-36.

So the domain is x>36

Range :

The range is every value that y or f(x) can take on.

y=1/sqrt(x-36)

Apply cross multiplication

sqrt(x-36) = 1/y

Apply square each side

x-36 = 1/y²

x = (1/y²) + 36

Here we calculated f(y) = x = (1/y²) + 36.

For negative values of y , y² gives positive values.

So f(y) is defined for all real numbers except at y=0

Domain of f(y) is (-∞ , 0)U(0 , ∞)

Domain of f(y) is equal to Range of y

So the Range is (-∞ , 0)U(0 , ∞).