7. Determine whether each of these functions is a bijection from R to R.a) f (x) = −3x + 4 b) f (x) = −3x2 + 7 c) f (x) = (x + 1)/(x + 2) d) f (x) = x5 + 1

Determine whether the following functions are bijective.(a) f : R → R, with y = f (x) = 3x + 52(b) f : R → R, with y = f (x) = (2x − 7)2(c) f : R → R, with y = f (x) = √3x − 1

1. Why is f not a function from R to R ifa) f (x) = 1/x? b) f (x) =x ? c) f (x) =2 1x  ?2. Determine whether f is a function from Z to R ifa) f (n) = ±n b) 2 1f n n  c) 214f n n 3. Find these valuesa)1.1   b)0.1   c)4   d)3.2  e)5.2   e)2   e)1 22 3      4. Determine whether each of these functions from {a, b, c, d} to itself is one-to-one (onto)a) f (a) = b, f (b) = a, f (c) = c, f (d) = db) f (a) = b, f (b) = b, f (c) = d, f (d) = cc) f (a) = d, f (b) = b, f (c) = c, f (d) = d5. Determine whether each of these functions from Z to Z is one-to-one (onto)a) f (n) = n − 1 b) f (n) = n2 + 1 c) f (n) = n3 d) 2nf n     6. Determine whether f : Z × Z → Z is onto ifa) f (m, n) = 2m − n b) f (m, n) = m2 − n2 c) f (m, n) = m + n + 1d) f (m, n) = |m| − |n| e) f (m, n) = m2 − 4 f) f (m, n) = m + n7. Determine whether each of these functions is a bijection from R to R.a) f (x) = −3x + 4 b) f (x) = −3x2 + 7 c) f (x) = (x + 1)/(x + 2) d) f (x) = x5 + 18. Let S = {−1, 0, 2, 4, 7}. Find f (S) ifa) f (x) = 1 b) f (x) = 2x + 1 c) 5xf x     

4. Determine whether each of these functions from {a, b, c, d} to itself is one-to-one (onto)a) f (a) = b, f (b) = a, f (c) = c, f (d) = db) f (a) = b, f (b) = b, f (c) = d, f (d) = cc) f (a) = d, f (b) = b, f (c) = c, f (d) = d

9. Let f be the function from R to R defined by f (x) = x2. Finda) f −1({1}) b) f −1({x | 0 < x < 1}) c) f −1({x | x > 4})

Let A=7,8,9 and B=7,8,9 and f is onto from A to B, then which of the following is correct?*f is bijectivef is surjectivef may or may not be bijectivef is into function