Show that the function f:R--->R defined by f(x)= sin^2x +cos^2x is neither one-one nor onto
Dear Student
f(x) = sin²x + cos²x = 1
For every value of x the value of f(x) = 1. Hence, function is not one-one
For every value of x the value of f(x) = 1. From the range R only one value has images on the domain. For a function to be onto all values of the range must match one or more values from the domain. Hence the given function is not onto.
Regards
f(x) = sin²x + cos²x = 1
For every value of x the value of f(x) = 1. Hence, function is not one-one
For every value of x the value of f(x) = 1. From the range R only one value has images on the domain. For a function to be onto all values of the range must match one or more values from the domain. Hence the given function is not onto.
Regards