yeah, it is correct and the reason is, both functions $0.01^x$ and $0.25^x$ are strictly decreasing for interval $(-\infty,\infty)$.
So, if we consider $f(x)=0.01^x + 0.25^x$
then $f(1) = 0.26$ and since both functions are decreasing.So, value of sum of both functions for $x>1$ will also be decreasing. So, $f(>1)$ will always be less than $0.26$ and this way, we can't get $0.7$. So, option (A) is eliminated.
Now, $f(0) = 2$. Now, when $x<0$, both functions will be strictly increasing and so their sum will also be increasing. So, $f(<0)$ will always be $>2$ and so we will not get $0.7$ for $x\leq 0$. So, option (C) eliminated.
Now, since, $f(0) = 2$ and $f(1) = 0.26$ and $f(x)$ is decreasing in $(-\infty,\infty)$and continuous function, so there must be some value of $x$ which is between $0$ and $1$ for which $f(x)$ will be $0.7$.