Answer: 19
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Work Shown:
Start with the inner function. Plug in x = 5
g(x) = x-2
g(5) = 5-2 ... Replace every x with 5
g(5) = 3
This means f(g(5)) = f(3) since we can replace g(5) with 3
Now plug x = 3 into the f(x) function
f(x) = 3x+10
f(3) = 3(3) + 10
f(3) = 19
Therefore, f(g(5)) = 19
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An alternate route is shown below
f(x) = 3x + 10
f(x) = 3(x) + 10
f(g(x)) = 3(g(x)) + 10 ... replace every x with g(x)
f(g(x)) = 3(x-2) + 10 ... replace g(x) on the right side with x-2
f(g(x)) = 3x-6+10 ... distribute
f(g(x)) = 3x+4
f(g(5)) = 3(5)+4 .... plug in x = 5
f(g(5)) = 19 .... we get the same answer