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.....


2 years ago

Share

### Answers : (1)

                    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 & RegardsJitender SinghIIT DelhiaskIITians Faculty

one month ago

More Questions On Differential Calculus

Have any Question? Ask Experts
Post Question

Vouchers
To Win!!!
Image attached . Find condition that equation shown in image has local minima at certain x belonging to R-

f’(x)= 3x 2 + 2ax+ b this eqauation will have real roots means there will be a local minima if d>=0 d= a 2 – 12 b=0 or greater than 0

 Sher Mohammad 21 days ago
Please tell how they calculate it sir please see attachment

Hello student, Please find answer to your question By binomial theorm,

 Jitender Singh 21 days ago
the force acting on moving charge particle in a uniform magnetic field is (a) normal to magnetic field (b) at 45 degree from the magnetic field (c) parallel to the magnetic field

Ans: Hello Student, Please find answer to your question below Force acting on a moving charged particle in a magnetic field is given by F = Magnetic Force v = velocity of a particle q =...

 Jitender Singh 3 days ago
Find the real values of the parameter ‘a’ for which atleast one complex number z =x+iy satisfies both the equality | z- ai | = a+4 and the inequality | z-2 |

Hello Student, Please find the answer to your question below [|z-ai| = a + 4] [|z-2| < 1] For these two to have atleast one solution, then both circles must intersect [|x+iy-ai| = a+4]...

 SHAIK AASIF AHAMED 5 days ago
If A-B perpendicular to B and |A-B|=A/2 angle between A,B is

B / / x degree /___________ A / 90\ / \ A/2 / x \ /____________\ -B A A-B let the angle between A and B vector be x. then we know A-B is perpendicular to B so its also perpendicular to -B....

 Akash Kumar Dutta one year ago

|A-B|=A/2 i.e. A 2 +B 2 - 2ABCos@ = A 2 /4------------>(1) also, (A-B).B = 0 as angle bwtween is 90 (dot product |a.b|=|a||b|Cos@ ) ABCos@ = B 2 ---------->(2) on substituting in (1)...

 gauhar singh one year ago

A-B PERPENDICULAR TO B LET ANGLE BETWEEN A AND B BE θ THEN BSinθ/(A-BCosθ)=tan 90degree=1/0 that gives A-BCosθ=0 A=BCosθ A/B=COSθ and also √A 2 +B 2...

 lokesh soni one year ago
A sphere is inscribed in a cube. Find the ratio of volume of sphere to volume of cube. Please give the solution

the radius of the sphere is equal to 1/2 the side of the cube (since, diameter of the cube is equal to the side of the cube let the radius be r then, volume of sphere...