Let-f-x-3-x-1-g-x-3-x-and-h-x-4-determine-the-values-of-x-for-which-f-x-g-x-h-x-

Question Number 70003 by Maclaurin Stickker last updated on 29/Sep/19

L e t f (x) = 3^{x - 1}, g (x) = 3^{x} a n d h (x) = 4

d e t e r m i n e t h e v a l u e s o f x f o r w h i c h :

f (x) + g (x) ⩾ h (x) .

Commented by Abdo msup. last updated on 30/Sep/19

f (x) + g (x) ⩾ 4 \Leftrightarrow 3^{x - 1} + 3^{x} ⩾ 4 \Leftrightarrow 3^{x} (3^{- 1} + 1) ⩾ 4

\Rightarrow (1 + \frac{1}{3}) 3^{x} ⩾ 4 \Rightarrow \frac{4}{3} 3^{x} ⩾ 4 \Rightarrow 3^{x - 1} ⩾ 1 \Rightarrow

l n (3^{x - 1}) ⩾ 0 \Rightarrow (x - 1) l n (3) ⩾ 0 \Rightarrow x ⩾ 1

Commented by Maclaurin Stickker last updated on 30/Sep/19

P e r f e c t .

Commented by Abdo msup. last updated on 11/Oct/19

t h a n k x