Answer to Question #129380 in Discrete Mathematics for jaya

Question

(b) Determine whether each of following functions are invertible. If it is an invertible, find
it’s inverse.
(i) f : R → R such that f(x) = 3x + 10
(ii) f : R → R such that f(x) = x
2
- 1

Answer 1

1) f(x) = 3x + 10

y=3x+10

x=(y-10)/3

INVERSE is x=(y-10)/3

2) f(x) = x²Â - 1

To find the inverse function, swap x and y, and solve the resulting equation for x.

If the initial function is not one-to-one, then the inverse function cannot be defined uniquely.

So, swap the variables: y=x²âˆ’1 becomes x=y²âˆ’1

Now, solve the equation x=y²âˆ’1 for y.

$y=- \sqrt{x + 1}; y= \sqrt{x + 1}$