IPMAT 2022 - Quantitative Aptitude Question 26

(81)^x + (81)^f(x) = 3
a^x > 0 for any value of x
So (81)^f(x) can take value (0, 3) based on which x will adjust itself to satisfy above relation & it can’t be equal to 3 as (81)^f(x)< 3
0 < (81)^f(x) < 3 
3^−∞ < 3^4f(x) < 3¹
− ∞ < 4f(x) < 1
− ∞ < f(x) < 1/4
f(x) ∈ (− ∞, 0.25)