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

**Solution:**

g(x) = y_{1} = x − 7 ….. (1)

f(x) = y_{2} = 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 y_{1} + 5 where y_{1} = 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.

## 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.