`f : R^(+) to R^(+) : f(x) = e^(x) ` isA. many-one and intoB. many -on – InterviewSolution

InterviewSolution

1.	`f : R^(+) to R^(+) : f(x) = e^(x) ` isA. many-one and intoB. many -one and ontoC. one-one and intoD. one-one and onto
Answer» Correct Answer - D `f(x_(1)) =f(x_(2)) rArr e^(x_(1)) =e^(x_(2)) rArr x_(1) =x_(2)` . So f is one-one For each `x in R^(+) EE " log " x in R^(+) s.t f(log x )=x` `So , f in onto.

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.