Question

Example 1.30 If : R - R is defined by f(x) = 2x - 3 prove that is a bijection and find its
inverse.
Solution:
Method 1:
One-to-one : Let fir) = f(u). Then 2.1-3 = 2y - 3; this implies that r = y. That is, (c) =
implies that r = y. Thus f is one-to-one.
Onto: Let y € R. Let r = Then S(r) = 20) - 3 = y. Thus f is onto. This al
be proved by saying the following statement. The range of f is R (how?) which is equal
co-domain and hence / is onto.
verse Let y = 2. - 3. Then y + 3 = 2.7 and hence r = Thus f-'(4)
2
2
+ 3
replacing y as 1, we get -'(7) =
2
y + 3​

Answer 1

Answer:

........ ..................