+91-735-322-1155
FlagBACK
Flag Differential Calculus> onto function...
question mark

if f:R->[pi/6,pi/2),f(x)= arcsin (x^2 - a/x^2 + 1) is a onto function,den set of values of a is.....

manuj mittal , 14 Years ago
Grade
anser 1 Answers
Jitender Singh
Ans:
y = sin^{-1}(x^{2}-\frac{a}{x^{2}}+1)
(x^{2}-\frac{a}{x^{2}}+1)=siny
x^{4}+(1-siny)x^{2}-a=0
This is simple Quadratic in x2,
\Delta \geq 0
(1-siny)^{2}\geq 4.(-a)
sin^{2}y-2siny+1+4a\geq 0
\Delta <0
4<4(4a+1)
a>0
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty
Last Activity: 11 Years ago
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Other Related Questions on differential calculus

question mark
the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution to  move once over to level a playground. find the area of the playground in square m?
differential calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
Find dy/DX when y=x^sinx+sin-1√x.
 
Please give me the solution of this problem. 
differential calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.
differential calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.
differential calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin C
where A + B + C = T
(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.
differential calculus
1 Answer Available

Last Activity: 3 Years ago