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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 function f given by f(x) = 2 - x - 5| is.
  • A
    Domain = $\mathrm{R}^{+}$, Range $= ( –\infty, 1]$
  • ✓
    Domain = R, Range $= ( –\infty, 2]$
  • C
    Domain = R, Range $= ( –\infty, 2]$
  • D
    Domain = $\mathrm{R}^{+}$, Range $= ( –\infty, 2]$
✓

Answer

Correct option: B.
Domain = R, Range $= ( –\infty, 2]$
  1. Domain = R, Range $= ( –\infty, 2]$
Solution:
We have, f(x) = 2 - |x - 5|
Clearly, f(x) is defined for all $\text{x}\in\text{R}.$
$\therefore$ Domain of f = R
Now, $|\text{x}-5|\geq0,\forall\text{x}\in\text{R}$
$\Rightarrow-|\text{x}-5|\leq0$
$\Rightarrow2-|\text{x}-5|\leq2$
$\therefore\text{f(x)}\leq2$
$\therefore$ Range of $\text{f}=(-\infty, 2]$

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