How do you find the domain and range of f(x) = 6/x - 4?

Solution:

Given, function f(x) = 6/(x - 4)

We have to find the domain and range of f(x).

The denominator of f(x) cannot be zero as this would make f(x) undefined.

Now, x - 4 = 0

⇒ x = 4

x cannot be equal to 4

Therefore, the domain is all real numbers except x = 4.

Let f(x) = y

⇒ y = 6/(x - 4)

⇒ y(x - 4) = 6

⇒ xy - 4y = 6

⇒ xy = 6 + 4y

⇒ x = (6 + 4y)/y

The denominator of x cannot be zero as this would make y undefined.

So, y cannot be equal to zero.

Therefore, the range is all real numbers except zero.

Therefore, domain = all real numbers except 4, range = all real numbers except zero.

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How do you find the domain and range of f(x) = 6/x - 4?

Summary:

The function f(x) = 6/(x - 4) has domain = all real numbers except 4, range = all real numbers except zero.