# Let f(x) = x+8 and g(x)=x^{2}-6x-7, what is f(g(2))?

**Solution:**

g(x) = y\(_1\)_{ }= x^{2 }- 6x - 7 ….. (1)

f(x) = y\(_2\)_{ }= x + 8 ….. (2)

f(g(x)) is a composite function that can be written as (fog)(x), where in the output values of g(x) are taken as its input values.

Where x is present in f(x) you should substitute y\(_1\)_{ }

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

f(g(x)) = y\(_1\) + 8 where y_{1 }= x^{2 }- 6x - 7

f(g(x)) = x^{2 }- 6x - 7 + 8

f(g(x)) = x^{2 }- 6x + 1

Now substitute x = 2 in f (g(x))

f(g(2)) = (2)^{2 }- 6(2) + 1

So we get

f(g(2)) = 4 - 12 + 1

f(g(-1)) = 5 - 12 = - 7

Therefore, f(g(x)) when x = 2 is - 7.

## Let f(x) = x+8 and g(x)=x^{2}-6x-7, what is f(g(2))?

**Summary:**

Let f(x) = x+8 and g(x)=x^{2}-6x-7, f(g(2)) is - 7.