Exactly how many function f: Q arrow Q exist such that f(x+ y)=f(x)+f(y) and f(x y)=f(x) f(y) for all x, y ∈ Q ?

Question

Exactly how many function f: Q arrow Q exist such that f(x+ y)=f(x)+f(y) and f(x y)=f(x) f(y) for all x, y ∈ Q ? (A) One (B) Two (C) Three (D) Infinitely many

Tardigrade Admin · Accepted Answer

These functions are simultaneously satisfy for f(x)=x and f(x)=0 ∀ x ∈ Q

Q. Exactly how many function $f : Q \to Q$ exist such that $f (x + y) = f (x) + f (y)$ and $f (x y) = f (x) f (y)$ for all $x, y \in Q$ ?

One

Two

Three

Infinitely many

These functions are simultaneously satisfy for $f (x) = x$ and $f (x) = 0 \forall x \in Q$

Q. Exactly how many function f:Q→Q exist such that f(x+y)=f(x)+f(y) and f(xy)=f(x)f(y) for all x,y∈Q ?

One

Two

Three

Infinitely many

These functions are simultaneously satisfy for f(x)=x and f(x)=0∀x∈Q

Q. Exactly how many function $f : Q \to Q$ exist such that $f (x + y) = f (x) + f (y)$ and $f (x y) = f (x) f (y)$ for all $x, y \in Q$ ?

These functions are simultaneously satisfy for $f (x) = x$ and $f (x) = 0 \forall x \in Q$