(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

The Answer to the Question
is below this banner.

Can't find a solution anywhere?

NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?

You will get a detailed answer to your question or assignment in the shortest time possible.

Here's the Solution to this Question

1) f(x) = 3x + 10

y=3x+10

x=(y-10)/3

INVERSE is x=(y-10)/3

2) f(x) = x2 - 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=x2−1 becomes x=y2−1

Now, solve the equation x=y2−1 for y.

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