Knowee
Questions
Features
Study Tools

Express your answer as a polynomial in standard form.f, of, x, equals, 2, x, squared, plus, 5, x, plus, 6f(x)=2x 2 +5x+6g, of, x, equals, 2, x, plus, 1g(x)=2x+1Find: , left parenthesis, f, circle, g, right parenthesis, left parenthesis, x, right parenthesisFind: (f∘g)(x)

Question

Express your answer as a polynomial in standard form.f, of, x, equals, 2, x, squared, plus, 5, x, plus, 6f(x)=2x 2 +5x+6g, of, x, equals, 2, x, plus, 1g(x)=2x+1Find: , left parenthesis, f, circle, g, right parenthesis, left parenthesis, x, right parenthesisFind: (f∘g)(x)

🧐 Not the exact question you are looking for?Go ask a question

Solution

Para encontrar (fg)(x)(f \circ g)(x), primero debemos entender que esto significa f(g(x))f(g(x)). Vamos a sustituir g(x)g(x) en la función f(x)f(x).

Dado: f(x)=2x2+5x+6f(x) = 2x^2 + 5x + 6 g(x)=2x+1g(x) = 2x + 1

Primero, sustituimos g(x)g(x) en f(x)f(x): f(g(x))=f(2x+1)f(g(x)) = f(2x + 1)

Ahora, sustituimos 2x+12x + 1 en cada xx de f(x)f(x): f(2x+1)=2(2x+1)2+5(2x+1)+6f(2x + 1) = 2(2x + 1)^2 + 5(2x + 1) + 6

Expandimos y simplificamos: Primero, calculamos (2x+1)2(2x + 1)^2: (2x+1)2=(2x+1)(2x+1)=4x2+4x+1(2x + 1)^2 = (2x + 1)(2x + 1) = 4x^2 + 4x + 1

Luego, sustituimos esto en la función: f(2x+1)=2(4x2+4x+1)+5(2x+1)+6f(2x + 1) = 2(4x^2 + 4x + 1) + 5(2x + 1) + 6

Distribuimos los coeficientes: =24x2+24x+21+52x+51+6= 2 \cdot 4x^2 + 2 \cdot 4x + 2 \cdot 1 + 5 \cdot 2x + 5 \cdot 1 + 6 =8x2+8x+2+10x+5+6= 8x^2 + 8x + 2 + 10x + 5 + 6

Combinamos términos semejantes: =8x2+18x+13= 8x^2 + 18x + 13

Por lo tanto, (fg)(x)=8x2+18x+13(f \circ g)(x) = 8x^2 + 18x + 13.

This problem has been solved

Similar Questions

Express your answer as a polynomial in standard form.f, of, x, equals, 2, x, squared, plus, 3, x, plus, 12f(x)=2x 2 +3x+12g, of, x, equals, 5, x, minus, 6g(x)=5x−6Find: , left parenthesis, g, circle, f, right parenthesis, left parenthesis, x, right parenthesisFind: (g∘f)(x)

Express your answer as a polynomial in standard form.f, of, x, equals, x, squared, plus, x, plus, 6f(x)=x 2 +x+6g, of, x, equals, 3, x, plus, 5g(x)=3x+5Find: , f, of, g, of, xFind: f(g(x))

Express your answer as a polynomial in standard form.f, of, x, equals, x, squared, plus, 6, x, plus, 8f(x)=x 2 +6x+8g, of, x, equals, minus, 3, x, minus, 10g(x)=−3x−10Find: , left parenthesis, f, circle, g, right parenthesis, left parenthesis, x, right parenthesisFind: (f∘g)(x)

Express your answer as a polynomial in standard form.f, of, x, equals, 5, x, minus, 4f(x)=5x−4g, of, x, equals, x, squared, minus, 3, x, minus, 11g(x)=x 2 −3x−11Find: , left parenthesis, f, circle, g, right parenthesis, left parenthesis, x, right parenthesisFind: (f∘g)(x)

Given the definitions of f, of, xf(x) and g, of, xg(x) below, find the value of left parenthesis, g, circle, f, right parenthesis, left parenthesis, 0, right parenthesis, .(g∘f)(0).f, of, x, equals, 2, x, squared, plus, 2, x, minus, 3f(x)=2x 2 +2x−3g, of, x, equals, minus, 5, x, plus, 3g(x)=−5x+3

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.