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  • The domain and range of the real function f defined by f (x) = is given by x −4

The domain and range of the real function f  defined by f(x) = \frac{4-x}{x-4}  is given by

    1. Domain = R, Range = \left \{-1, 1\right \}
    2. Domain = R - \left \{1\right \}, Range = R
    3. Domain = R - \left \{4\right \}, Range = \left \{- 1\right \}
    4. Domain = R - \left \{- 4\right \}, Range = \left \{-1, 1\right \}

Answers (1)

Given data: y=f(x) = \frac{4-x}{x-4}

 

We know that, the domain of f(x) = R-\left \{4\right \}

Thus, yx - 4y = 4-x

yx+x = 4y+4

x(y+1) = 4y+4

x = 4(1+y)/1+y

Now, if x is a real no. then,

1+y \neq 0

Thus, y \neq -1

Thus, the range off(x) = R - (-1)

Thus, opt (c) is the correct answer.

Posted by

infoexpert21

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