Prove that the function f : R → R defined by f (x) = 2x + 5 is on… - Vidyadip

Question

Prove that the function f : R → R defined by f (x) = 2x + 5 is one-one.

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Answer

Note that a function f is one-one if
f(x₁ ) = f (x₂ ) $\Rightarrow$ x₁ = x₂ (definition of one-one function)
Now, given that f (x₁ ) = f (x₂ ), i.e., 2x₁ + 5 = 2x₂ + 5
$\Rightarrow$ 2x₁ + 5 – 5 = 2x₂ + 5 – 5 (adding the same quantity on both sides)
2x₁ + 0 = 2x₂ + 0
2x₁ = 2x₂( using additive identity of real number)
$\frac{2}{2} x_{1}=\frac{2}{2} x_{2}$ dividing by the same non zero quantity
x₁ = x₂
Hence, the given function is one one

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