Question

The domain of the function $$\sqrt {{x^2} - 5x + 6} + \sqrt {2x + 8 - {x^2}} $$       is :

A. $$\left[ {2,\,3} \right]$$
B. $$\left[ { - 2,\,4} \right]$$
C. $$\left[ { - 2,\,2} \right] \cup \left[ {3,\,4} \right]$$  
D. $$\left[ { - 2,\,1} \right] \cup \left[ {2,\,4} \right]$$
Answer :   $$\left[ { - 2,\,2} \right] \cup \left[ {3,\,4} \right]$$
Solution :
$$f\left( x \right) = \sqrt {\left( {x - 2} \right)\left( {x - 3} \right)} + \sqrt { - \left( {x - 4} \right)\left( {x + 2} \right)} $$
The first part is real outside $$\left( {2,\,3} \right)$$  and the second is real in $$\left[ { - 2,\,4} \right]$$  so that the domain is $$\left[ { - 2,\,2} \right] \cup \left[ {3,\,4} \right].$$

Releted MCQ Question on
Calculus >> Function

Releted Question 1

Let $$R$$ be the set of real numbers. If $$f:R \to R$$   is a function defined by $$f\left( x \right) = {x^2},$$   then $$f$$ is:

A. Injective but not surjective
B. Surjective but not injective
C. Bijective
D. None of these.
View Answer
Releted Question 2

The entire graphs of the equation $$y = {x^2} + kx - x + 9$$     is strictly above the $$x$$-axis if and only if

A. $$k < 7$$
B. $$ - 5 < k < 7$$
C. $$k > - 5$$
D. None of these.
View Answer
Releted Question 3

Let $$f\left( x \right) = \left| {x - 1} \right|.$$    Then

A. $$f\left( {{x^2}} \right) = {\left( {f\left( x \right)} \right)^2}$$
B. $$f\left( {x + y} \right) = f\left( x \right) + f\left( y \right)$$
C. $$f\left( {\left| x \right|} \right) = \left| {f\left( x \right)} \right|$$
D. None of these
View Answer
Releted Question 4

If $$x$$ satisfies $$\left| {x - 1} \right| + \left| {x - 2} \right| + \left| {x - 3} \right| \geqslant 6,$$       then

A. $$0 \leqslant x \leqslant 4$$
B. $$x \leqslant - 2\,{\text{or}}\,x \geqslant 4$$
C. $$x \leqslant 0\,{\text{or}}\,x \geqslant 4$$
D. None of these
View Answer

Practice More Releted MCQ Question on
Function

Practice More MCQ Question on Maths Section

AlgebraSequences and SeriesQuadratic EquationComplex NumberMatrices and DeterminantsPermutation and CombinationBinomial TheoremMathematical InductionMathematical Reasoning
Statistics and ProbabilityStatisticsProbability
CalculusSets and RelationsFunctionLimitsContinuityDifferentiability and DifferentiationApplication of DerivativesDifferential EquationsIndefinite IntegrationDefinite IntegrationApplication of Integration
GeometryStraight LinesCircleParabolaEllipseHyperbolaLocus3D Geometry and VectorsThree Dimensional Geometry
TrigonometryTrigonometric Ratio and IdentitiesTrignometric EquationsProperties and Solutons of TriangleInverse Trigonometry Function