Home
Class 12
MATHS
If the function f:[2, oo)rarr[1, oo) is...

If the function `f:[2, oo)rarr[1, oo)` is d defined by `f(x)=3^(x(x-2))`, then `f^(-1)(x)` is

A

`1+sqrt(1+log_(3)x)`

B

`1-sqrt(1+log_(3)x)`

C

`1-sqrt(1-log_(3)x)`

D

Does not exist

Text Solution

Verified by Experts

The correct Answer is:
A
Let g(x) be the inverse of f, then `f (g(x)) = x`
`rArr 3^(g(x)(g(x)-2))=x rArr (g(x))^(2)-2g(x)-log_(3)x=0`
`rArr g(x)=(2+sqrt(4+4log_(3)x))/(2)=+-1 sqrt(1+log_(3)x)`
Since `g.[1, oo] to [2,oo]`
So `g(x)=1+sqrt(1+log_(3))x`
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 8

    VMC MODULES ENGLISH|Exercise MATHMATICS (SECTION 2)|5 Videos

  • MOCK TEST 7

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • MOCK TEST 9

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

Similar Questions

Explore conceptually related problems

If f:[1, oo) rarr [1, oo) is defined as f(x) = 3^(x(x-2)) then f^(-1)(x) is equal to

Let f:[4,oo)to[4,oo) be defined by f(x)=5^(x^((x-4))) .Then f^(-1)(x) is

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

Find the inverse of the function: f:[1, oo) rarr [1,oo),w h e r ef(x)=2^(x(x-2))

If f : [0, oo) rarr [2, oo) be defined by f(x) = x^(2) + 2, AA xx in R . Then find f^(-1) .

Let f:(-oo,2] to (-oo,4] be a function defined by f(x)=4x-x^(2) . Then, f^(-1)(x) is

The function f:R rarr R defined as f(x)=(x^(2)-x+1)/(x^(2)+x+1) is

If f : [0, oo) rarr [0, oo) and f(x) = (x^(2))/(1+x^(4)) , then f is

The function f : (0, oo) rarr [0, oo), f(x) = (x)/(1+x) is

Consider the function f:(-oo,oo)rarr(-oo,oo) defined by f(x)=(x^2-ax+1)/(x^2+ax+1), 0ltalt2 , and let g(x)=int_0^(e^x) (f\'(t)dt)/(1+t^2) . Which of the following is true? (A) g\'(x) is positive on (-oo,0) and negative on (0,oo) (B) g\'(x) is negative on (-oo,0) and positive on (0,oo) (C) g\'(x) changes sign on both (-oo,0) and (0,oo) (D) g\'(x) does not change sign on (-oo,oo)