Given that f(x) = 2x + 1 and g(x) = -5x + 2, solve for f(g(x)) when x = 3 ?

Solution:

g(x) = - 5x + 2 ….. (1)

f(x) = 2x + 1 ….. (2)

f(g(x)) can be written as (fog)(x), which is a composite function.

Take the g(x) values as inputs and find (fog)(x)

⇒ substituting equation (1) in x which is present in equation (2)

f(g(x)) = 2(g(x)) + 1

f(g(x)) = 2 (- 5x + 2) + 1

f(g(x)) = -10x + 4 + 1

f(g(x)) = -10x + 5

Now substitute x = 3 in f (g(x))

f(g(x)) = -10 (3) + 5

So we get

f(g(x)) = - 30 + 5 = - 25

Therefore, f(g(x)) when x = 3 is - 25.

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Given that f(x) = 2x + 1 and g(x) = -5x + 2, solve for f(g(x)) when x = 3 ?

Summary:

Given that f(x) = 2x + 1 and g(x) = -5x + 2, f(g(x)) when x = 3 is - 25.