Home
Class 12
MATHS
Let f: defined from (1//4,oo) to R^(+) a...

Let f: defined from `(1//4,oo) to R^(+) as, f(x)=log_(1//4)(x-(1)/(4))+(1)/(2)log_(4)(16x^(2)-8x+1)`
Statement-1: f(x) is neither injective nor surjective .
Statement-1: f(x) is a constant function.

A

Statement-1 is true, statement -2 is true and statement -2 is correct explantion for statement-1.

B

Statement-1 is true, statement -2 is true and statement -2 is NOT correct explantion for statement-1.

C

Statement-1 is true, statement-2 is false

D

Statement-1 is false, statement-2 is true

Text Solution

Verified by Experts

B
`f(x)=log_(1//4)(x-(1)/(4))+(1)/(2) log_(4)16+(1)/(2) log_(4)(x^(2)-(x)/(2)+(1)/(16))(x gt(1)/(4))`
`=log_(1//4)(x-(1)/(4))+1+log_(4)(x-(1)/(4))`
`=-log_(4)(x-(1)/(4))+log_(4)(x-(1)/(4))+1`
`=1 implies ` f is constant
hence f is many one as well into. Also range is a singelton `implies` f is constant but a constant function can be any thing `implies` not the explanation.
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    BANSAL|Exercise MATHS SECTION-3 Part-A [ Multiple correct choice type ]|5 Videos

  • TEST PAPERS

    BANSAL|Exercise MATHS SECTION-3 Part-B[ Matrix type ]|2 Videos

  • TEST PAPERS

    BANSAL|Exercise MATHS SECTION-3 Part-A [ comprehension type ]|3 Videos

  • PROBABILITY

    BANSAL|Exercise All Questions|1 Videos

  • THERMODYNAMICS

    BANSAL|Exercise Match the column|7 Videos

Similar Questions

Explore conceptually related problems

Let f:R rarr R defined by f(x)=(x^(2))/(1+x^(2)) . Proved that f is neither injective nor surjective.

The domain of the function f(x)=log_(1//2)(-log_(2)(1+1/(root(4)(x)))-1) is:

The function f(x)=cos^(-1)((|x|-3)/(2))+(log_(e)(4-x))^(-1) is defined for

Domain of definition of the function f(x)=log_(2)(-log_((1)/(2))(1+x^(-4))-1) is

Let f : R to and f (x) = (x (x^(4) + 1) (x+1) +x ^(4)+2)/(x^(2) +x+1), then f (x) is :

The domain of the function f(x)=log_((3)/(2))log_((1)/(2))log_(pi)log_((pi)/(4))x is

Let A={x:x varepsilon R-}f is defined from A rarr R as f(x)=(2x)/(x-1) then f(x) is (a) Surjective but nor injective (b) injective but nor surjective (c) neither injective surjective (d) injective

Statement-1 : f : R rarr R, f(x) = x^(2) log(|x| + 1) is an into function. and Statement-2 : f(x) = x^(2) log(|x|+1) is a continuous even function.

If f(x) is continuous at x=1 , where f(x)=(log_(2)2x)^(1/(log_(2)x) , for x!=1 , then f(1)=

Find the range of the function f(x)=log_(2)(4^(x^(2))+4^((x-1)^(2)))