Solve
Find (f o g)(-6) when f(x)=4x+4 and g(x)=6x^2-3x-6.
I originally came up with 918, but the answer is 916. Obviously I was close, but could someone tell how to get 916. I am studying for a test and am re-working my homework problems. Thanks.
Set your problem up
-6=4x=4 -6=6^2-3x-6
work these out
g(-6) = 6*36 - 3*(-6) -6
= 228
f(228) = 4(228)+4
=912 +4 = 916
To find (f o g)(-6), we need to substitute -6 into function g(x) first, and then substitute the result into function f(x). Let's go step by step:
1. Start by evaluating g(-6) using the function g(x) = 6x^2 - 3x - 6.
Plug in -6 for x:
g(-6) = 6(-6)^2 - 3(-6) - 6
Simplify:
g(-6) = 6(36) + 18 - 6
g(-6) = 216 + 18 - 6
g(-6) = 228 - 6
g(-6) = 222
2. Now that we have the value of g(-6), substitute it into f(x) = 4x + 4:
Plug in 222 for x:
f(g(-6)) = 4(222) + 4
f(g(-6)) = 888 + 4
f(g(-6)) = 892
Therefore, (f o g)(-6) = 892.
Your original answer of 918 was close, but there was an error in evaluating g(-6) as 228 instead of the correct value of 222. By substituting the correct result into f(x), we get the correct answer of 892, not 916.