# How to determine whether f(x)3sin2x +5 is one-to-one function. How to find the inverse of the function?

Apr 18, 2018

NOTE -

1) Use the fact that a function is one-one iff it is MONOTONIC.

2) Inverse function is possible for only one-one function.

#### Explanation:

The given function $f \left(x\right) = 3 \sin \left(2 x\right) + 5$ is non-monotonic .

$\therefore$ This is not a one-one function.

The graph of this function is given below :-

graph{3sin(2x)+5 [-25.66, 25.67, -12.83, 12.83]}
OR

You can use another test to check if it is not one-one function :-

Draw a horizontal line parallel to X-axis which goes through the graph ;
if it cuts the graph at more than one point then it is not one-one function.

This is not an Invertible function since it is NOT one-one function.