Home
Class 12
MATHS
Let f(x)a n dg(x) be two continuous func...

Let `f(x)a n dg(x)` be two continuous functions defined from `RvecR` , such that `f(x_1)` > `f(x_2)` and `g(x_1)` < `g(x_2)` `for all` `x_1`>`x_2` `dot` Then what is the solution set of `f(g(alpha^2-2alpha)` > `f(g(3alpha-4))`

Text Solution

Verified by Experts

From the given information ,f is increasing and g is decreasing in R.
Now `f(g(alpha)^(2)-2alpha)gtf(g(3alpha-4))`
since f is increasing we, have
`g(a)^(2)-2(alpha)gt g(3alpha-4)`
`rarr(alpha)^(2)-5alpha+4lt0`
`rarr (alpha-1)(alpha-4)lt0`
`rarr` a in`(1,4)
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Solved Examples|20 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Concept Application Exercise 6.1|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

If f(x) and g(x) are two continuous functions defined on [-a,a] then the the value of int_(-a)^(a) {f(x)f+(-x) } {g(x)-g(-x)}dx is,

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) .

Let f be the continuous and differentiable function such that f(x)=f(2-x), forall x in R and g(x)=f(1+x), then

Let f (x) and g (x) be two differentiable functions, defined as: f (x)=x ^(2) +xg'(1)+g'' (2) and g (x)= f (1) x^(2) +x f' (x)+ f''(x). The value of f (1) +g (-1) is:

Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-f(x)=xdot Then the value of f(3) is 2 b. 3 c. 4 d. 5

Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-f(x)=xdot Then the value of f(3) is 2 b. 3 c. 4 d. 5

f(x) and g(x) are two differentiable functions in [0,2] such that f"(x)=g"(x)=0, f'(1)=2, g'(1)=4, f(2)=3, g(2)=9 then f(x)-g(x) at x=3/2 is

Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)=sqrt(9-x^2)dot Then describe each of the following function: g-f

Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)=sqrt(9-x^2)dot Then describe each of the following function: g/f

Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)=sqrt(9-x^2)dot Then describe each of the following function: f+g