# Let f(x) = x-2 and g(x) = x^{2}-7x-9. What is f(g(-1))?

**Solution:**

g(x) = y\(_1\) = x^{2 }- 7x - 9 ….. (1)

f(x) = y\(_2\)_{ }= x - 2 ….. (2)

f(g(x)) is a composite function can be written as (fog)(x), where f(g) takes all the output values of g(x) as its input values.

⇒where x is present in f(x), you should plug-in y\(_1\)

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

f(g(x)) = y\(_1\)_{ }- 2 where y\(_1\)_{ }= x^{2 }- 7x - 9

f(g(x)) = x^{2 }- 7x - 9 - 2

f(g(x)) = x^{2 }- 7x - 11

Now substitute x = -1 in f (g(x))

f(g(-1)) = (-1)^{2 }- 7(-1) - 11

So we get

f(g(-1)) = 1 + 7 - 11

f(g(-1)) = 8 - 11 = - 3

Therefore, f(g(x)) when x = -1 is - 3.

## Let f(x) = x-2 and g(x) = x^{2}-7x-9. What is f(g(-1))?

**Summary:**

Let f(x) = x-2 and g(x) = x^{2}-7x-9. f(g(-1)) is - 3.