Let f: RrightarrowR be a continuous and ...

Let `f: RrightarrowR` be a continuous and differentiable function such that `(f(x^2+1))^(sqrt(x))=5forAAx in (0,oo),` then the value of `(f((16+y^2)/(y^2)))^(4/(sqrt(y))) ` for each y in `(0,oo)` is equal to

125

625

Text Solution

Verified by Experts

The correct Answer is:

`(f((16+y^(2))/(y^(2))))^((4)/(sqrt(y)))=(f((16)/(y^(2))+1))^((4)/(sqrt(y)))`
`=(f(((4)/(y^(2)))^(2)+1))^((4)/(sqrt(y)))`
`=[(f(((4)/(y^(2)))^(2)+1))^((2)/(sqrt(y)))]^(2)`
`=5^(2)`

Topper's Solved these Questions

RELATIONS AND FUNCTIONS
CENGAGE|Exercise Exercise (Multiple)|27 Videos
RELATIONS AND FUNCTIONS
CENGAGE|Exercise Exercise (Comprehension)|32 Videos
RELATIONS AND FUNCTIONS
CENGAGE|Exercise Exercise 1.15|8 Videos
Quadratic Equations, Inequalities, Modulus and Logarithms
CENGAGE|Exercise Question Bank|31 Videos
SCALER TRIPLE PRODUCTS
CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Let f: RvecR be a continuous and differentiable function such that (f(x^2+1))^(sqrt(x))=5forAAx in (0,oo), then the value of (f((16+y^2)/(y^2)))^(4/(sqrt(y)))fore a c hy in (0,oo) is equal to 5 (b) 25 (c) 125 (d) 625

Let f(x) be continuous and differentiable function everywhere satisfying f(x+y)=f(x)+2y^(2)+kxy and f(1)=2, f(2)=8 then the value of f(3) equals

If f(x) be a differentiable function such that f(x+y)=f(x)+f(y) and f(1)=2 then f'(2) is equal to

Let f(x) be continuous and differentiable function for all reals and f(x + y) = f(x) - 3xy + ff(y). If lim_(h to 0)(f(h))/(h) = 7 , then the value of f'(x) is

Let f(x) be a non-constant twice differentiable function defined on (oo,oo) such that f(x)=f(1-x) and f'(1/4)=0^(@). Then

Let f(x) be a differentiable function satisfying f(y)f((x)/(y))=f(x)AA,x,y in R,y!=0 and f(1)!=0,f'(1)=3 then

Let f be a differentiable function satisfying f(x+2y)=2yf(x)+xf(y)-3xy+1 AA x , y in R such that f'(0)=1 ,then value of f(8) is equal

Let y=f(x) be a continuous function such that (dy)/(dx)=|x-1|* If y(0)=0 then y(3) equals

CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Single)

If f(x) is a polynomial satisfying f(x)f(1/x)=f(x)+f(1/x)a n df(3)=28 ...
Text Solution
|
If f(2x+y/8,2x-y/8)=x y , then f(m , n)=0 only when m=n only when m!...
Text Solution
|
Let f : R to R be a function such that f(0)=1 and for any x,y in R, f(...
Text Solution
|
If f(x+y)=f(x)+f(y)-x y-1, AA x , y in R and f(1)=1, then the number ...
Text Solution
|
The function f satisfies the functional equation 3f(x)+2f((x+59)/(x1))...
Text Solution
|
Let f: RrightarrowR be a continuous and differentiable function such t...
Text Solution
|
Let g(x)=f(x)-1. If f(x)+f(1-x)=2AAx in R , then g(x) is symmetrical ...
Text Solution
|
If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) ...
Text Solution
|
If f(x+1/2)+f(x-1/2)=f(x)fora l lx in R , then the period of f(x) is ...
Text Solution
|
If a f(x+1)+b f(1/(x+1))=x,x !=-1,a != b,then f(2) is equal to
Text Solution
|
If f(3x+2)+f(3x+29)=AAx in R , then the period of f(x) is
Text Solution
|
If the graph of y=f(x) is symmetrical about the lines x=1a n dx=2, the...
Text Solution
|
If f(x)= maximum {x^3,x^2,1/64} AA x in[0,oo) then
Text Solution
|
The equation ||x-2|+a|=4 can have four distinct real solutions for x i...
Text Solution
|
Number of integral values of k for which the equation 4 cos^(-1)(-|x|)...
Text Solution
|
If f(x) is a real-valued function defined as f(x)=In (1-sinx), then t...
Text Solution
|
Let f(x)=x+2|x+1|+x-1|dotIf f(x)=k has exactly one real solution, then...
Text Solution
|
The number of solutions of 2 cosx=|sinx|, 0 le x le 4 pi, is
Text Solution
|
Let f1(x)={x, x leq x leq 1 and 1 x gt1 and 0,otherwise f2(x) =f1 (...
Text Solution
|
If log(4)((2f(x))/(1-f(x)))=x, " then "(f(2010)+f(-2009)) is equal to
Text Solution
|