We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
326
1
avatar+1206 

Let $f(x) = 3x-8$ and $g(f(x)) = 2x^2 + 5x - 3.$ Find $g(-5).$

 Jul 14, 2018
 #1
avatar+7683 
+1

First we will need to find g(x).

\(g(3x-8) = 2x^2+5x-3\\ \quad g(x) \\= g\left(3\left(\dfrac{x+8}{3}\right)-8\right) \\= 2\left(\dfrac{x+8}{3}\right)^2+5\left(\dfrac{x+8}{3}\right)-3\\ =\dfrac{2}{9}\left(x^2+16x+64\right)+\dfrac{5}{3}(x+8)-3\\ =\dfrac{2}{9}x^2 +\dfrac{47}{9}x+\dfrac{221}{9}\)

Therefore g(-5) = \(\dfrac{2}{9}(-5)^2+\dfrac{47}{9}(-5)+\dfrac{221}{9}=\dfrac{50-235+221}{9} = \dfrac{36}{9} = 4\)

Ans = 4.

 Jul 15, 2018

12 Online Users

avatar