To determine the properties of f(x)=10x, we need to check if the function is one-one (injective) and onto (surjective).
A function is one-one if f(x1)=f(x2) implies x1=x2.
Suppose f(x1)=f(x2)
10x1=10x2
x1=x2
Therefore, f is one-one.
A function f:R→R is onto if for every real number y, there exists an x such that f(x)=y.
Let y be any real number. Solve for x:
f(x)=y
10x=y
x=10y
Since y is a real number, 10y is also a real number. Every real number can be achieved as an output.
Therefore, f is onto.
Since f(x)=10x is both one-one and onto, the function is bijective.