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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

1 answer

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.