Question

Given that f(x) = x2 – 3x – 54 and g(x) = x + 6, find (f.g)(x) and

express the result in standard form.

Answer 1

To find (f.g)(x), substitute g(x) into f(x) and simplify the expression.

Step-by-step explanation:

To find (f.g)(x), we need to substitute g(x) into f(x).

So, (f.g)(x) = f(g(x)) = f(x + 6).

By substituting x + 6 into f(x), we get:

(f.g)(x) = (x + 6)2 - 3(x + 6) - 54.

Expanding the expression gives:

(f.g)(x) = x2 + 12x + 36 - 3x - 18 - 54.

Combining like terms, we have:

(f.g)(x) = x2 + 9x - 36.

Therefore, (f.g)(x) expressed in standard form is x2 + 9x - 36.