Express your answer as a polynomial in standard form.

Question

f, of, x, equals, 2, x, squared, plus, 3, x, minus, 6
f(x)=
2x
2
+3x−6
g, of, x, equals, minus, 4, x, plus, 10
g(x)=
−4x+10
Find: , g, of, f, of, x
Find: g(f(x))

Answer 1

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

We are given: \[ f(x) = 2x^2 + 3x - 6 \] and \[ g(x) = -4x + 10 \]

Now we find \( g(f(x)) \): \[ g(f(x)) = g(2x^2 + 3x - 6) \]

Now we will substitute \( 2x^2 + 3x - 6 \) into \( g(x) \): \[ g(f(x)) = -4(2x^2 + 3x - 6) + 10 \]

Now, we distribute \(-4\): \[ = -4 \cdot 2x^2 - 4 \cdot 3x - 4 \cdot (-6) + 10 \] \[ = -8x^2 - 12x + 24 + 10 \]

Now, combine like terms: \[ = -8x^2 - 12x + 34 \]

Thus, the expression for \( g(f(x)) \) in standard polynomial form is: \[ \boxed{-8x^2 - 12x + 34} \]