Is it possible to figure out the coefficients of an exponential equation given a certain number of points? For exponential equations in the form of: $$f(x) = a^x + b^x ,$$ is it possible to solve for a and b if you have a certain number of points? The answers to the similar question here pertain to equations in the form of $f(x)=ae^{bx}$, and this question pertains to $f(x) = ab^x$, but it's not clear to me whether similar techniques can be used on $f(x) = a^x + b^x$.

$$f(x) = a^x + b^x $$

You need two equations to solve for both $a$ and $b$.

$$f(x_1)=c=a^{x_1}+b^{x_1}$$

and

$$f(x_2)=d=a^{x_2}+b^{x_2}$$

Of course, there are some obvious restrictions on what points can be used to yield unique solutions.

$$x_1 \
ot = x_2 \
ot =0 $$

Of course, in all likelihood, you'll end up having to solve these equations using numerical methods.