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1. Show that the function f: R → R defined by f(x) = 2x – 3 is one-one and onto. Find f-1

2. Which of the following figure represents the graph of a function on R which is onto but not one-one.

3. Write a function on R which is onto but not one-one

1 Answer

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Best answer

1. f(x) = 2x – 3

f(x1) = f(x2)

⇒ 2x1 – 3 = 2x2 – 3 ⇒ x1 = x2

Therefore f is one-one.

Let f(x) = yeR, then

y = 2x – 3 ⇒ 2x = y + 3 ⇒ x = \(\frac{y+3}{2}\) ∈ R

Therefore f is onto. Then f-1(x) = \(\frac{x+3}{2}\).

2. Option (c)
[(b),(c),(d) are not one-one since for different values of x, we have same value of y. ie; horizontal line meets at more than one point, (b) and (d) are not onto since range and codomain are different].

3. f(x) = x2, f : R → [0, ∞) (Any other function).

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