Mathematics Test 77

Result

Mathematics Test 77

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Weekly Quiz Competition

Question 1
4 / -1

If ; f(x) = sin^–1(x²-a / x²+a) is a onto function; then set of value of "a" is

A
{–1/2}

B
{–1/2, 1}

C
(–1, ∞)

D
(–∞, ∞)
Question 2
4 / -1

If g(x) = x² + x – 2

1/2 (gof) (x) = 2x² – 5x + 2

then ƒ(x) is equal to :-

A
2x – 3

B
2x + 3

C
2x² + 3x + 1

D
2x² – 3x – 1

Solution

g(x) = x² + x – 2

⇒ (gof) (x) = g[ƒ(x)] = [ƒ(x)]² + ƒ(x) – 2

Given, 1/2 (gof) (x) = 2x² – 5x + 2.

∴ 1/2 [ƒ(x)]² + 1/2 ƒ(x) – 1 = 2x² – 5x + 2

⇒ [ƒ(x)]² + ƒ(x) = 4x² – 10x + 6

⇒ ƒ(x) [ƒ(x) + 1] = (2x – 3) [(2x – 3) + 1]

⇒ ƒ(x) = 2x – 3
Question 3
4 / -1

If f : R →R ; f(x) = 2x+1,g : R → R, g(x) = x³,then (fog)^–1 (55) equals

A
27

B
3

C
-27

D
-3
Question 4
4 / -1

If y = sin^–1x + tan^–1x + sec^–1x then set of values of y is

A
[π/4, 3π/4]

B
[- 3π/4, 3π/4]

C
{π/4, 3π/4}

D
[-π/4, π/4]
Question 5
4 / -1

sin^–1(sin10) + sin^–1(sin12) + cos^-1 (-1/2) =

A
2 - π/3

B
22 + 3π/3

C
2 + π/3

D
None of these