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

Solution:

Given that:

f(x) = x − 2 ---------- (1)

g(x) = x² − 7x − 9 ----------- (2)

Both f(x) and g(x) are the function of x and thus depend on x. 

We have to find the 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 − 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)) is -3.

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

Summary:

Let f(x) = x - 2 and g(x) = x² - 7x - 9, then f(g(-1)) is -3.