Express your answer as a polynomial in standard form.

Question

f, of, x, equals, 2, x, squared, minus, 4, x, minus, 11
f(x)=
2x
2
−4x−11
g, of, x, equals, minus, 5, x, plus, 14
g(x)=
−5x+14
Find: , g, of, f, of, x
Find: g(f(x))

Answer 1

To find \( g(f(x)) \), we first have to express \( f(x) \) fully and then substitute it into \( g(x) \).

We have:

\[ f(x) = 2x^2 - 4x - 11 \] \[ g(x) = -5x + 14 \]

Next, we substitute \( f(x) \) into \( g(x) \):

\[ g(f(x)) = g(2x^2 - 4x - 11) \]

Now, replacing \( x \) in \( g(x) \):

\[ g(f(x)) = -5(2x^2 - 4x - 11) + 14 \]

Distributing \( -5 \):

\[ = -5 \cdot 2x^2 + 20x + 55 + 14 \] \[ = -10x^2 + 20x + 69 \]

Now, writing this in standard form:

\[ g(f(x)) = -10x^2 + 20x + 69 \]

So the final answer is:

\[ \boxed{-10x^2 + 20x + 69} \]