Functions Question 370
Question: Find the domain of $ f(x)=\sqrt{{{(0.625)}^{4-3x}}-{{(1.6)}^{x(x+8)}}} $
Options:
A) $ [-3,2] $
B) $ [1,4] $
C) $ [2,5] $
D) $ [-4,-1] $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Clearly, $ {{(0.625)}^{4-3x}}\ge {{(1.6)}^{x(x+8)}} $ or $ {{( \frac{5}{8} )}^{4-3x}}\ge {{( \frac{8}{5} )}^{x(x+8)}} $ or $ {{( \frac{8}{5} )}^{3x-4}}\ge {{( \frac{8}{5} )}^{x(x+8)}} $ or $ 3x-4\ge x^{2}+8x $ or $ x^{2}+5x+4\le 0 $ or $ -4\le x\le -1 $ Hence, the domain of function $ f(x) $ is $ x\in [-4,-1] $
BETA
