Question

fie functiile f, g:R sa se determine f(2),g(5), f(2)+f(0), Fog, gof, fof, fog(5) , dacă:
a) f(x) =6x-5, g(x) =1/6x+5/6
b) f(x) =3x-5, g(x) =x²-2
URGENT!

Answer 1

Răspuns:

Explicație pas cu pas:

f , g : R --> R

a) f(x) = 6x-5 ; g(x) = 1/6 · x +5/6 = x/6 + 5/6 = (x+5)/6

f(2) = 6·2-5 = 12-5 = 7

g(5) = (5+5)/6 = 10/6 = 5/3

f(0) = 6·0-5 = -5

f(2)+f(0) = 7-5 = 2

f o g = f(g(x)) = 6[(x+5)/6] -5 = x+5-5 = x

g o f = g(f(x)) = (6x-5+5)/6 = 6x/6 = x

f o f = f(f(x)) = 6(6x-5)-5 = 36x-30-5 = 36x-35

f o g(5) = f(g(5))

g(5) = 5/3 =>

f o g(5) = 6·5/3 -5 = 30/3 - 5 = 10-5 = 5

b)  f(x) = 3x-5, g(x) = x²-2

f(2) = 3·2-5 = 6-5 = 1

g(5) = 5²-2 = 25-2 = 23

f(0) = 3·0-5 = -5

f(2)+f(0) = 1-5 = -4

f o g = 3(x²-2) -5 = 3x²-11

g o f = (3x-5)²-2 = 9x²-30x+25-2 = 9x²-30x+23

f o f = 3(3x-5) -5 = 9x-15-5 = 9x-20

g(5) = 23

f o g(5) = 3·23-5 = 64

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