Question 533724
What is a, if f(a)=8, and f(x)=2^-x

Substitute a for x in the second equation:  f(a) = 2^-a

Set it equal to the solution for f(a)

2^-a = 8

Recall that with exponents, that if x^y = x^z then y=z.  Often to solve such problems we have to express the constant (in this case 8) in terms of the same base as the term with the exponent (in this case 2).

8 = 2^3.  So we can rewrite this equation as:

2^-a = 2^3

Recall that with exponents, that if x^y = x^z then y=z.

-a = 3 divide both sides by -1 so   a=-3