If f(x) = 3x + 10 and g(x) = x - 2, Find f(g(5))

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

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