finding the returns to scale of a production function Find the returns to scale for he following production function- $(x_1 + 1)^.5 (x_2)^.5$

My attempt,
Let $f(x_1,x_2)=(x_1 + 1)^.5 (x_2)^.5$
And $g(x_1,x_2)=(x_1)^.5 (x_2)^.5$
Now,
$(x_1 + 1)^.5 (x_2)^.5$ 
$&gt;$
$(x1)^.5 (x_2)^.5$
Therefore,
$f(x_1,x_2)&gt;g(x_1,x_2)$
Or, $f(tx_1,tx_2)&gt;g(tx_1,tx_2)$ for some t>0
$&gt;(tx_1)^.5 (tx_2)^.5$
$=t(x_1)^.5 (x_2)^.5$
$=tg(x_1,x_2)$
The function g exhibits constant returns to scale. The function f being bigger than it should exhibit increasing returns to scale. The answer given, however, is decreasing returns to scale. Where am I wrong? Thank you in advance.
What you have proven is that $$f(tx_1, tx_2) &gt; tg(x_1,x_2)$$

which translates "scaled $f$ is higher than some other, homogeneous function $g$ scaled by the same factor". This does not prove anything about the returns to scale related to $f$, although I can see why it may appear otherwise.

You can go in reverse, starting from 

$$tf(x_1,x_2) = t^{0.5}t^{0.5}f(x_1,x_2)=...$$

and compare to $f(tx_1, tx_2)$. 

Also beware about the following: what are the permissible values for $t$ when returns are not constant? Are you sure we should obtain the result for $t&gt;0$, or maybe we examine the property for a smaller interval?