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RELATIONS AND FUNCTIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSRELATIONS AND FUNCTIONS1 Mark
MCQ
Choose the correct answers: The domain and range of the real function f defined by $\text{f(x)}=\frac{4-\text{x}}{\text{x}-4}$ is given by.
  • A
    Domain = R, Range = {-1, 1}
  • B
    Domain = R - {1}, Range = R
  • ✓
    Domain = R - {4}, Range = {-1}
  • D
    Domain = R - {-4}, Range = {-1, 1}
✓

Answer

Correct option: C.
Domain = R - {4}, Range = {-1}
Given that: $\text{f(x)}=\frac{4-\text{x}}{\text{x}-4}$
We know that f(x) is defined if $\text{x}-4\neq0 \Rightarrow \text{x}\neq4$
So, the domain of f(x) is = R - {4}
Let $\text{f(x)}=\text{y}=\frac{4-\text{x}}{\text{x}-4}$
$\Rightarrow\text{yx}-4\text{y}=4-\text{x}\Rightarrow\text{yx}+\text{x}=4\text{y}+4$
$\Rightarrow\text{x}(\text{y}+1)=4\text{y}+4\Rightarrow\text{x}=\frac{4(1+\text{y})}{1+\text{y}}$
If x is real number, then $1+\text{y}\neq0\Rightarrow\text{x}\neq1$
$\therefore$ Range of f(x) = R - {-1)

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