No, f is not a linear transformation.
A linear transformation must satisfy the following two properties:
f(u + v) = f(u) + f(v) for all u, v in the domain of f.
f(kv) = kf(v) for all k in the field and v in the domain of f.
Property 1 is not satisfied by f.
For example, f(2 + 3) = f(5) = 153, but f(2) + f(3) = 63 + 63 = 126.
Therefore, f is not a linear transformation.
Question
Let f: R R be defined by f(3) = 63. Is f a linear transformation? a. f(+ y) = f(2) + f(y) = + Does f(x + y) = f(x) + f(y) for all 2, y e R?