Given that f(x) = 2x + 5 and g(x) = x − 7, solve for f(g(x)) when x = −3.

Solution:

g(x) = y₁ = x − 7 ….. (1)

f(x) = y₂ = 2x + 5 ….. (2)

f(g(x)) is a composite function and can be written as (fog)(x)

Where x is present in f(x) you should substitute y1

I.e., substituting equation (1) in x which is present in equation (2)

f(g(x)) = 2 y₁ + 5 where y₁ = x − 7

f(g(x)) = 2 (x - 7) + 5

f(g(x)) = 2x - 14 + 5

f(g(x)) = 2x - 9

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

f(g(x)) = 2 (-3) - 9

So we get

f(g(x)) = - 6 - 9 = - 15

Therefore, f(g(x)) when x = -3 is - 15.

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Given that f(x) = 2x + 5 and g(x) = x − 7, solve for f(g(x)) when x = −3.

Summary:

Given that f(x) = 2x + 5 and g(x) = x − 7, f(g(x)) when x = -3 is - 15.