Related InterviewSolutions

• Two functions f and g are defined on the set of real numbers `RR` by , `f(x)= cos x and g(x) =x^(2)` , then, `(f o g)(x)=`A. `cos ^(2)x`B. `cos x^(2)`C. ` sin^(2) x`D. `sin x^(2)`
• Let the mapping `f:[0. infty) rarr [0,2]` be defined by, `f(x)=(2x)/(x+1)` then mapping f will be ____A. injective but not surjectiveB. neither injective nor surjectiveC. onto but not one-oneD. one-one and into
• The domain for which the functions `f(x)=3x^(2)-2x` and `g(x)=3(3x-2)` are equal will be ___A. `{1,(2)/(3)}`B. `{1,3}`C. `{(2)/(3),(3)}`D. `{(2)/(3),3}`
• State which of the following statement is false ?A. If `A ={0,1,2,3},B={-3,-2,-1,0,1} and f:A rarr B ` is the mapping defined by `f(x)=x-3` for all `x in A`, then f is a one-one mappingB. A constant mapping will be 0ne-one when its domain constans only one element.C. Functions f and g are defined as follows:`f:RR-{2} rarrRR,` where `f(x)=(x^(2)-4)/(x-2) and g:RR rarrRR,` where `g(x)=x+2,` then `f=g`D. `f(x)=sqrt(x^(2)+4x-1)` then `f(-2)` is not exist.
• Let the function `f:RR rarr RR` be defined by `f(x)=x^(2) (RR` being the set of real numbers), then f is __A. many - one and onto mappingB. one-one and onto mappingC. one-one and into mappingD. many-one and into mapping
• Let the function `f:RR rarr RR` be defined by , `f(x)=3x-2 and g(x)=3x-2 (RR` being the set of real numbers), then `(f o g)(x)=`A. `7x-8`B. `9x-7`C. `9x-8`D. `8x-9`
• The mapping `f:ZZ rarr ZZ` defined by , `f(x)=3x-2`, for all `x in ZZ`, then f will be ___A. onto but not one-oneB. one-one but not ontoC. many-one and intoD. many-one and onto
• Let RR be the set of real numbers and the mapping `f: RR rarr RR` be defined by `f(x)=2x^(2)`, then `f^(-1) (32)=`A. `{4,-4}`B. `{1,-1}`C. `{2,-2}`D. `{3,-3}`
• If the function `f:RR rarr RR and g: RR rarr RR` are given by `f(x)=3x+2` and `g(x)=2x-3 (RR` being the set of real numbers), state which of the following is the value of `(g o f) (x)`?A. `6x-7`B. `6x+1`C. 3x+5D. `6x+4`
• Let the function `f:A rarr B` have an inverse function `f^(-1): B rarr A`, then the nature of the function f is __A. one-one and ontoB. one-one and intoC. many-one and ontoD. many-one and into