Which one of the following function is surjective but not injective? (A) `f:R -> R, f(x) = x^3 + x + 1` (B)`f : [0, oo) -> (0, 1], f(x) = e^|x|` (C) `f: R -> R`, `f(x) = x^3 + 2x^2 - x + 1` (D) `f: R -> R+, f(x) = sqrt(1+ x^2)`

Which of the following function is surjective but not injective. (a) f:R->R ,f(x)=x^4+2x^3-x^2+1 (b) f:R->R ,f(x)=x^3+x+1 (c) f:R->R^+ ,f(x)=sqrt(x^2+1) (d) f:R->R ,f(x)=x^3+2x^2-x+1

Which of the following function is surjective but not injective. (a) f:R->R ,f(x)=x^4+2x^3-x^2+1 (b) f:R->R ,f(x)=x^2+x+1 (c) f:R->R^+ ,f(x)=sqrt(x^2+1) (d) f:R->R ,f(x)=x^3+2x^2-x+1

Which of the following function is surjective but not injective. (a) f:R->R ,f(x)=x^4+2x^3-x^2+1 (b) f:R->R ,f(x)=x^2+x+1 (c) f:R->R^+ ,f(x)=sqrt(x^2+1) (d) f:R->R ,f(x)=x^3+2x^2-x+1

Which of the following function is surjective but not injective.(a) f:R rarr R,f(x)=x^(4)+2x^(3)-x^(2)+1(b)f:R rarr R,f(x)=x^(2)+x+1(c)f:R rarr R^(+),f(x)=sqrt(x^(2)+1)(d)f:R rarr R,f(x)=x^(3)+2x^(2)-x+1

Which of the following are one-one ,onto (or) bijections? Justify your answer. (i) f: R to R, f(x) =(2x+1)/3 (ii) f: N to N, f(x) = 2x+3 (iii) f:[0, infty) to [0,infty), f(x) = x^(2) (iv) f: R to R, f(x) =x^(2) (v) f: R to (0, infty), f(x) = 5^(x) (vi) f: (0, infty) to R, f(x) = log_(e)^(x) (vii) f: R to R, f(x) = {{:(x, if x gt 2),(5x-2, if x le 2):}

Check the injectivity and surjectivity of the following functions . f: R rarr R , f(x) = x^(2) -2

Check the following functions for one-one and onto (a) f:R rarr R, f(x)=(2x-3)/(7) (b) f:R rarr R, f(x)=|x+1| (c) f:R-{2} rarr R, f(x)=(3x-1)/(x-2) (d) f:R-{-1,1}, f(x)=sin^(2)x .

Classify the following functions f(x) defined in R to R as injective , surjective , both or none . f(x) = x^(2)

Which of the following functions is one-one ? (1)f:R->R defined as f(x)=e^(sgn x)+e^(x^2) (2) f:[-1,oo) ->(0,oo) defined by f(x)=e^(x^2+|x|) (3)f:[3,4]->[4,6] defined by f(x)=|x-1|+|x-2|+|x-3|+x-4| (4) f(x) =sqrt(ln(cos (sin x))

Which of the following functions is one-one ? (1)f:R->R defined as f(x)=e^(sgn x)+e^(x^2) (2) f:[-1,oo) ->(0,oo) defined by f(x)=e^(x^2+|x|) (3)f:[3,4]->[4,6] defined by f(x)=|x-1|+|x-2|+|x-3|+x-4| (4) f(x) =sqrt(ln(cos (sin x))