Question

Show that the function \(f:R\to R\) given by \(f(x)=x^3\) is injective.

Answer 1

f: R \(\to\) R is given as \(f(x)=x^3.\) 
Suppose f(x) = f(y), where x, y ∈ R. \(\Rightarrow\) x³ = y³ … (1) 
Now, we need to show that x = y. 
Suppose x ≠ y, their cubes will also not be equal. x³ ≠ y³ 
However, this will be a contradiction to (1). 
∴ x = y 
Hence, f is injective.