why use non-linear activation function

If we do not apply a Activation function then the output signal would simply be a simple linear function.A linear function is just a polynomial of one degree. Now, a linear equation is easy to solve but they are limited in their complexity and have less power to learn complex functional mappings from data. A Neural Network without Activation function would simply be a Linear regression Model, which has limited power and does not performs good most of the times. We want our Neural Network to not just learn and compute a linear function but something more complicated than that. Also without activation function our Neural network would not be able to learn and model other complicated kinds of data such as images, videos , audio , speech etc. That is why we use Artificial Neural network techniques such as Deep learning to make sense of something complicated ,high dimensional,non-linear -big datasets, where the model has lots and lots of hidden layers in between and has a very complicated architecture which helps us to make sense and extract knowledge form such complicated big datasets. we need to apply a Activation function f(x) so as to make the network more powerfull and add ability to it to learn something complex and complicated form data and represent non-linear complex arbitrary functional mappings between inputs and outputs. Hence using a non linear Activation we are able to generate non-linear mappings from inputs to outputs.