Given that, f : R → R be the function defined by
f (x) = sin (3x+2) ∀ x ∈R
f is invertible if it is bijective that is f should be one-one and onto.
Now, we know that sin x lies between -1 and 1.
So, the range of f(x) = sin (3x+2) is [-1,1] which is not equal to its co-domain.
i.e., range of f ≠ R (co-domain)
In other words, range of f is less than co-domain, i.e there are elements in co-domain which does not have any pre-image in domain.
so, f is not onto.
Hence, f is not invertible.
Rate this question :