Home
Class 12
MATHS
Let f(x) is a polynomial satisfying f(x)...

Let `f(x)` is a polynomial satisfying `f(x).f(y) = f(x) +f(y) + f(xy) - 2 ` for all `x, y` and `f(2) = 1025,` then the value of `lim_(x->2) f'(x)` is

A

`5.2^(8)`

B

`5.2^(9)`

C

`5.2^(7)`

D

`5.2^(10)`

Text Solution

Verified by Experts

The correct Answer is:
D
Given `f(x).f(y)= f(x) +f(y) +f(xy) -2`
Put `y=(1)/(x)`
`rArr {f(1)}^(2) =3f(1)-2`
`rArr {f(1)}^(2) -3f(1)+2=0`
`rArr (f(1)-1) (f(1)-2)=0`
`rArr f(1)=1,2`
`rArr f(1)=2, ( :' f(1) ne 1)`
`:.f(x).f((1)/(x))=f(x)+f((1)/(x))+2-2`
`rArr f(x).f((1)/(x))=f(x)+f((1)/(x))`
`rArr f(x)=1 pm x^(n)`
`:. f(2)=1 pm 2^(n)=1025`
`rArr 2^(n)=1024=2^(10)`
`rArr n=10`
`:.f(x)=1+x^(10)`
`rArr f'(x)=10x_(9)`
`:.lim_(x to 2) f'(x)=lim_(x to 2)10xx x^(9)=10xx2^(9)=5 xx 2^(10)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x) is a polynomial satisfying f(x)*f(y)=f(x)+f(y)+f(xy)-2 for all x,y and f(2)=1025, then the value of lim_(x rarr2)f'(x) is

If f(x) a polynomial function satisfying f(x)f(y)=f(x)+f(y)+f(xy)-2 for all real x and y and f(3)=10 ,then f(4)-8 is equal

If f(2(x)/(y))=f(2x)-f(y) for all x,y>0 and f(3)=2, then the value of [f(7)], is

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(xy)AA x,y in R and if f(2)=5, then find the value of f(f(2))

If f (x) a polynomial function satisfying f (x) f (y) = f (x) + f(y) + f (xy) all real x and y and f(3) = 10, then f (4) – 8 is equal to

Let f (x) be a function satisfying f (x) f (y) = f (xy) for all real x, y. If f (2) = 4, then what is the value of f((1)/(2)) ?

let f(x) be the polynomial function. It satisfies the equation 2 +f(x)* f(y) = f(x) + f(y) +f(xy) for all x and y. If f(2) =5 find f|f(2)| .