Let f(x) = x + 8 and g(x) = x² - 6x - 7. Find f(g(2)).

Solution:

Given, f(x) = x + 8

g(x) = x² - 6x - 7

We have to find f(g(2)).

f(g(x)) = f(x² - 6x - 7)

= (x² - 6x - 7) + 8

= x² - 6x - 7 + 8

f(g(x)) = x² - 6x + 1.

Put x = 2 in the above expression,

f(g(2)) = (2)² - 6(2) + 1

= 4 - 12 + 1

= 5 - 12

f(g(2)) = -7

Therefore, the value of f(g(2)) is -7.

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Let f(x) = x + 8 and g(x) = x² - 6x - 7. Find f(g(2)).

Summary:

Let f(x) = x + 8 and g(x) = x² - 6x - 7. The value of f(g(2)) is -7.