Explicación paso a paso:
Sean las funciones:
f(x) = 5x + 10
g(x) = -4 + 3x²
Determine:
f o g(x) = f ( g (x) )
g o f(x) = g ( f (-7) )
Resolvamos:
a)
( f o g )(x) = f ( g (x) )
( f o g )(x) = 5(-4 + 3x²) + 10
( f o g )(x) = -20 + 15x² + 10
( f o g )(x) = 15x²-20 + 10
( f o g )(x) = 15x² -10
b)
( g o f )(-7) = g ( f (x) )
( g o f )(-7) = -4 + 3(5x + 10)²
( g o f )(-7) = -4 + 3(5(-7) + 10)²
( g o f )(-7) = -4 + 3(-35+ 10)²
( g o f )(-7) = -4 + 3(-25)²
( g o f )(-7) = -4 + 3(625)
( g o f )(-7) = -4 + 1875
( g o f )(-7) = 1871
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Explicación paso a paso:
Sean las funciones:
f(x) = 5x + 10
g(x) = -4 + 3x²
Determine:
f o g(x) = f ( g (x) )
g o f(x) = g ( f (-7) )
Resolvamos:
a)
( f o g )(x) = f ( g (x) )
( f o g )(x) = 5(-4 + 3x²) + 10
( f o g )(x) = -20 + 15x² + 10
( f o g )(x) = 15x²-20 + 10
( f o g )(x) = 15x² -10
b)
( g o f )(-7) = g ( f (x) )
( g o f )(-7) = -4 + 3(5x + 10)²
( g o f )(-7) = -4 + 3(5(-7) + 10)²
( g o f )(-7) = -4 + 3(-35+ 10)²
( g o f )(-7) = -4 + 3(-25)²
( g o f )(-7) = -4 + 3(625)
( g o f )(-7) = -4 + 1875
( g o f )(-7) = 1871