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If f(x) = -x2 – 1, and
g(x) = x + 5, then
f(g(x)) = –x2 + [ ? ]x + [ ]

Sagot :

Mhanifaidn

Answer:

  • - x² - 10x - 26

Step-by-step explanation:

Given:

  • f(x) = - x² - 1
  • g(x) = x + 5

Find f(g(x)):

  • f(g(x)) =
  • f(x + 5) =
  • - (x + 5)² - 1 =
  • - x² - 10x - 25 - 1 =
  • - x² - 10x - 26

[tex]\\ \tt\hookrightarrow f(x)=-x^2-1[/tex]

[tex]\\ \tt\hookrightarrow g(x)=x+5[/tex]

Now

[tex]\\ \tt\hookrightarrow f(g(x))[/tex]

  • Put g(x) value

[tex]\\ \tt\hookrightarrow f(x+5)[/tex]

[tex]\\ \tt\hookrightarrow -(x+5)^2-1[/tex]

[tex]\\ \tt\hookrightarrow -(x^2+10x+25)-1[/tex]

[tex]\\ \tt\hookrightarrow -x^2-10x-25-1[/tex]

[tex]\\ \tt\hookrightarrow -x^2-10x-26[/tex]

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