Question

Use the functions below.

f(x)=−3x+5


g(x)=2x2−11


What is (g ∘ f)(x)?


(1 point)
Responses

2x2−3x−6
2 x squared minus 3 x minus 6

−6x3+10x2+33x−55
negative 6 x cubed plus 10 x squared plus 33 x minus 55

−6x2+38
negative 6 x squared plus 38

18x2−60x+39

Answer 1

To find \((g \circ f)(x)\), which is \(g(f(x))\), we first need to evaluate \(f(x)\) and then substitute that result into \(g(x)\).

1. **Calculate \(f(x)\):**
\[
f(x) = -3x + 5
\]

2. **Substitute \(f(x)\) into \(g(x)\):**
\[
g(x) = 2x^2 - 11
\]
So,
\[
g(f(x)) = g(-3x + 5) = 2(-3x + 5)^2 - 11
\]

3. **Expand \((-3x + 5)^2\):**
\[
(-3x + 5)^2 = (-3x)^2 + 2 \cdot (-3x) \cdot 5 + 5^2 = 9x^2 - 30x + 25
\]

4. **Substitute this back into \(g(f(x))\):**
\[
g(f(x)) = 2(9x^2 - 30x + 25) - 11 = 18x^2 - 60x + 50 - 11
\]
\[
= 18x^2 - 60x + 39
\]

Therefore, \((g \circ f)(x) = 18x^2 - 60x + 39\).

The correct response is:
**18x² − 60x + 39**.