Let f(x) = x − 2 and g(x) = x² − 7x − 9. Find f(g(−1)).

We will use the concept of functions to solve the given question.

Answer: If f(x) = x − 2 and g(x) = x² − 7x − 9, then f(g(-1)) = -3.

Let us solve it step by step.

Explanation:

Given:

f(x) = x − 2 ------------ (1)

g(x) = x² − 7x − 9 ------------- (2)

Both f(x) and g(x) are functions of x and dependent on x. 

We have to find composite function f(g(x)).

f(g(x)) = {g(x)} - 2

⇒ f(g(x)) = (x² − 7x − 9) - 2 [From (1) and (2)]

⇒ f(g(x)) = x² − 7x − 9 - 2

⇒ f(g(x)) = x² − 7x − 11

Now let us solve this for x = -1.

f(g(-1)) = (-1)² − 7(-1) − 11

⇒ f(g(-1)) = 1 + 7 - 11 

⇒ f(g(-1)) = -3

Thus, if f(x) = x − 2 and g(x) = x² − 7x − 9, then f(g(-1)) = -3.