Question

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

Answer 1

$\huge\star\mathfrak\pink{{Answer:-}}$

$\large\star\bold\red{{PROOF:-}}$

Solution A function is one-one

if f(x1) = f(x2) ⇒ x1 = x2

.Using this we have to show that

“2x1+ 5 = 2x2 + 5” ⇒ “x1 = x2

”. This is of the formp ⇒

q, where, p is 2x1+ 5 = 2x2+ 5 and q : x1 = x2

. We have proved this in Example 2of “direct method”.We can also prove the same by using contrapositive of the statement. Nowcontrapositive of this statement is ~ q ⇒ ~ p, i.e., contrapositive of “ if f (x1) = f (x2),

then x1 = x2” is “if x1 ≠x2, then f(x1) ≠ f (x2)”.

Now x1 ≠ x 2

⇒ 2x1 ≠ 2x2

⇒ 2x1+ 5 ≠ 2x2 + 5

⇒ f (x1) ≠ f (x2).

Thank you