A function f:R→R defined by f(x) = 3 - 4x is-

one-one only onto only one-one and onto both neither one-one nor onto.

one-one and onto both

We have f: R→R defined by f(x) = 3 - 4x Let x1, x2 ∈R such that f(x1) = f(x2) ⇒3 - 4x1 = 3 -4 x2 ⇒ - 4x1 =  -4 x2 ⇒ x1 =  x2 so f is one-one. For any real number (y) in R, there exist {(3- y)/4} in R such that f{(3-y)/4} = 3 - 4{(3- y)/4} = y so f is onto. Hence f is one-one onto.