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

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Answer 1 · 2018-04-18T09:32:50

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.

The given function #f(x)=3sin(2x)+5# is non-monotonic .

#:.# 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.