Home
Class 12
MATHS
If f(x)=x^2+x+3/4 and g(x)=x^2+a x+1 be ...

If `f(x)=x^2+x+3/4` and `g(x)=x^2+a x+1` be two real functions, then the range of `a` for which `g(f(x))=0` has no real solution is `(-oo,-2)` b. `(-2,2)` c. `(-2,oo)` d. `(2,oo)`

A

`(-oo,-2)`

B

`(-2,2)`

C

`(-2,oo)`

D

`(2,oo)`

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)=x^(2)+x+(3)/(4)=(x+(1)/(2))^(2)+(1)/(2)ge(1)/(2)`
`g(f(x))=f(x)^(2)+af(x)+1`
for g(f(x))=0,
`a=-(f(x)+(1)/(f(x)))le-2`
`therefore` If `a gt -2, g(f(x))=0` has no solutions
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|9 Videos

  • FUNCTIONS

    CENGAGE ENGLISH|Exercise Comprehension Type|7 Videos

  • EQUATION OF PLANE AND ITS APPLICATIONS -II

    CENGAGE ENGLISH|Exercise DPP 3.4|14 Videos

  • GETTING STARTED WITH GRAPHS

    CENGAGE ENGLISH|Exercise Exercises 1.18|1 Videos

Similar Questions

Explore conceptually related problems

If f(x)=x^2+x+3/4 and g(x)=x^2+a x+1 be two real functions, then the range of a for which g(f(x))=0 has no real solution is (A) (-oo,-2) (B) (-2,2) (C) (-2,oo) (D) (2,oo)

Let f(x)=x^2 and g(x) = 2x + 1 be two real functions. find (f +g)(x) , (f-g)(x) , (fg)(x) , (f/g)(x) .

If f : [2,oo) to R be the function defined by f(x)=x^(2)-4x+5, then the range of f is

Let f(x) = x^(2) + 2x +5 and g(x) = x^(3) - 1 be two real functions. Find (f+g)(x), (f-g)(x), (fg)(x) and ((f)/(g))(x) .

Let f(x)=x^2 and g(x)" "=" "2x" "+" "1 be two real functions. Find (f" "+" "g) (x) , (f" "" "g)" "(x) , (fg)" "(x) , (f/g)(x) .

For x^2-(a+3)|x|=4=0 to have real solutions, the range of a is a (-oo,-7]uu[1,oo) b (-3,oo) c (-oo,-7] d [1,oo)

For x^2-(a+3)|x|+4=0 to have real solutions, the range of a is a. (-oo,-7]uu[1,oo) b. (-3,oo) c. (-oo,-7) d. [1,oo)

If f:[3,oo)toR is a function defined by f(x)=x^(2)-2x+6 , then the range of f is

If f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,where ac !=0, then prove that f(x)g(x)=0 has at least two real roots.

For x^2-(a+3)|x|-4=0 to have real solutions, the range of a is a) (-oo,-7]uu[1,oo) b) (-3,oo) c) (-oo,-7] d) [1,oo)