Question

Express your answer as a polynomial in standard form

ہے
f(x) = x² - x - 1
g(x) =
-
=-x-4
Find: f(g(x))

Answer 1

Explanation:

To find f(g(x)), we need to first find g(x) and then use the result to evaluate f(g(x)).

We are given:

g(x) = -x - 4

Now, we substitute this expression for g(x) into the expression for f(x):

f(g(x)) = f(-x - 4)

= (-x - 4)² - (-x - 4) - 1 [substituting g(x) = -x - 4 in f(x)]

= (x² + 8x + 16) - (-x - 4) - 1 [expanding the square term]

= x² + 9x + 11

Therefore, f(g(x)) = x² + 9x + 11.