How to show $f(x,y) \leq \theta f(x,y) + (1-\theta)f(x,y)$ for $\theta \in [0,1]$?

Question

Let $\theta \in [0, 1]$. Let $f(x,y)$ be a function. Is there a way I could prove that $f(x,y) \leq \theta f(x,y) + (1-\theta)f(x,y)$?

I have tried to start with $f(x,y) = 2f(x,y) - f(x,y)$ or similar simple equalities but I only find dead ends.

I could not find any counter examples.

Answer 1

$\theta f(x,y)+(1-\theta)f(x,y) = (1-\theta+\theta)f(x,y) = f(x,y)$

This is trivial if I understood your question correct.