Find the domain and range of the following real functionsf(x)=\(\frac{

1.	Find the domain and range of the following real functionsf(x)=\(\frac{4-x}{x-4}\)
Answer» Given, f (x) = \(\frac{4-x}{x-4}\) Domain: Clearly, f (x) is defined for all x ∈ R expect x = 4 ∴ Domain of f = R – {4 } = (−∞, 4),∪ (4, ∞) Range: Let y = f(x) ⇒y = \(\frac{4-x}{x-4}\) ⇒ y = \(\frac{-(x-4)}{x-4}\) = −1 ∴ Range of f = {– 1}

Find the domain and range of the following real functionsf(x)=\(\frac{4-x}{x-4}\)

Answer»

Given, f (x) = \(\frac{4-x}{x-4}\)

Domain: Clearly, f (x) is defined for all x ∈ R expect

x = 4

∴ Domain of f = R – {4 } = (−∞, 4),∪ (4, ∞)

Range: Let y = f(x)

⇒y = \(\frac{4-x}{x-4}\)

⇒ y = \(\frac{-(x-4)}{x-4}\) = −1

∴ Range of f = {– 1}