SOLUTION: I was sick when my teacher explained this so now i'm confused and don't know what to do. Please help me solve this equation: If f(x)=|x-8| and g(x)=4x+9 then g(f(2))=?

Algebra ->  Functions -> SOLUTION: I was sick when my teacher explained this so now i'm confused and don't know what to do. Please help me solve this equation: If f(x)=|x-8| and g(x)=4x+9 then g(f(2))=?      Log On


   

Question 540936: I was sick when my teacher explained this so now i'm confused and don't know what to do.
Please help me solve this equation: If f(x)=|x-8| and g(x)=4x+9 then g(f(2))=?
Found 2 solutions by AnlytcPhil, Theo:
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = |x-8| and g(x) = 4x+9 then g(f(2))=?

We find f(2) and then we substitute that for x in g(x) = 4x+9 

First find f(2), by substituting 2 for x in

f(x) = |x-8|

f(2) = |2-8|
f(2) = |-6|
f(2) = 6

Now substitute f(2) for x in the left side of g(x) = 4x+9 and 6 in the right
side of g(x) = 4x+9

   g(x) = 4x+9

g(f(2)) = 4(6)+9

g(f(2)) = 24 + 9

g(f(2)) = 33

Edwin

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = |x-8|
f(2) = |2-8| = |-6| = 6
g(x) = 4x + 9
g(6) = 4(6) + 9
g(6) = 24 + 9
g(6) = 33
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|x-8| means the absolute value of (x-8).
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g((f(x)) means you find the value of f(x) first and then use that value in g(x).
using a value means you replace x with that value.
if f(x) = 5*x, then f(3) = 5*3.
x is replaced with 3..
f(7) would be equal to 5*7 because x is replaced with 7.
f(g(x)) would equal to 5*(g(x)) because x is replaced with (g(x)).
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in the above, we solved for f(2) by replacing x with 2 to get |2-8| which gave us |-6| which gave us 6 (the absolute value of an expression is always positive).
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since g(x) = 4 * x + 9, then:
g(f(2)) becomes 4 * f(2) + 9 which becomes 4 * 6 + 9 because f(2) is equal to 6.
this then becomes 24 + 9 which becomes 33.