The set of all possible values of $f(x)$ for which $(81)^{x}+(81)^{f(x)}=3$ is

Question and options

The set of all possible values of

f(x)

for which

(81)^{x}+(81)^{f(x)}=3

Correct answer: C - $(-\infty, 0.25)$

81^f(x)=3-81^x and 81^x ranges over (0,inf), so 81^f lies in (0,3); f < log81 3 = 1/4. Range (-inf,0.25).