Compose

Algebra Level pending
  • f ( x ) = x 2 + 4 f(x)=x^2+4
  • h ( x ) = x 3 h(x)=x^3
  • f ∘ g ( x ) = h ( x ) f\circ g(x)=h(x)
  • g ( 5 ) = ? g(5)=?
13 \sqrt{13} 9 9 11 11 121 121

Camilo García Malagón by Camilo García Malagón , 22, Colombia

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2 solutions

Hung Woei Neoh
May 10, 2016

f ∘ g ( x ) = h ( x ) ( g ( x ) ) 2 + 4 = x 3 ( g ( x ) ) 2 = x 3 − 4 g ( x ) = x 3 − 4 g ( 5 ) = 5 3 − 4 = 121 = 11 f\circ g(x) = h(x)\\ (g(x))^2 + 4 = x^3\\ (g(x))^2 = x^3 - 4\\ g(x) = \sqrt{x^3 - 4}\\ g(5) = \sqrt{5^3 - 4} = \sqrt{121} = \boxed{11}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Kay Xspre
Mar 27, 2016

Since f ( g ( x ) ) = h ( x ) f(g(x)) = h(x) , we substitute x = 5 x = 5 , which gives ( g ( 5 ) ) 2 + 4 = 5 3 (g(5))^2+4 = 5^3 or simply g ( 5 ) = ± 11 g(5) = \pm11

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Functions cannot have two images for a single object

Hung Woei Neoh - 5 years, 1 month ago

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