If the function,`f:[1,oo]to [1,oo]` is defined by `f(x)=3^(x(x-1))`, t – InterviewSolution

InterviewSolution

1.	If the function,`f:[1,oo]to [1,oo]` is defined by `f(x)=3^(x(x-1))`, then `f^(-1)(x)` isA. `((1)/(3))^(x^((x-1)))`B. `(1)/(2){1-sqrt(1+4log_(3)x)}`C. `(1)/(2){1+sqrt(1+4log_(3)x)}`D. not defined
Answer» Correct Answer - C It can be checked that f is a bijection and hence invertible. Now, `fof^(-1)=x` `Rightarrow f(f^(-1)(x))=x` `Rightarrow 3^(f^(-1)(x)(f^(-1)(x)-1))=x` `Rightarrow f^(-1)(x)(f^(-1)(x)-1)=log_(3)x` `Rightarrow (f^(-1)(x))^(2)-f^(-1)(x)-log_(3)x=0` `Rightarrow f^(-1)(x)=(1)/(2){1+sqrt(1+4 log _(3)x)}" "[therefore f^(-1)(x) ge 1]`

Discussion

No Comment Found

Related InterviewSolutions

Find fog and gof, if (i) f(x) = ex, g(x) = loge x(ii) f(x) = x2, g(x) = cos x(iii) f(x) = |x|, g(x) = sin x(iv) f(x) = x + 1, g(x) = ex(v) f(x) = sin−1 x, g(x) = x2
Write the names of any two C++ header files.
List the names of any two functions of iostream.h header file.
Pick the odd one out from the following and give reason.gets() getline() getch() getchar()
What is the main function of iostream.h header file?
In a C++ program, you forgot to include the header file iostream.h. What are the possible errors occur in that Program? Explain ?
Let ` f(x) =sqrt(9-x^(2))." then , dom " (f ) =?`A. `[-3,3]`B. `(-oo,-3]`C. `[3,oo)`D. `(-oo,-3] uu (4,oo)`
Let `f(x)=sqrt(cos x).` Then dom (f ) =?A. `[0.(pi)/(2)]`B. `[(3pi)/(2),2pi]`C. `[0,(pi)/(2)]uu[(3pi)/(2),2pi]`D. none of these
Let `f(x) = log (1-x) +sqrt(x^(2)-1). `Then dom (f )=?A. `(1,oo)`B. `(-oo,-1]`C. `[-1,1]`D. `(0,1)`
Let `A={1,2}andB={2,4,6}."Let "f={x,y):x""inA,yinBandandygt2x+1}`. Write f as a set of ordered paris. Show that f is a relation but not a function from A to B.