16 uždavinys
Duotos funkcijos f (x) = x2 ir g(x) = x + 1.
16.1. Raskite funkcijos h(x) = f (g(x)) reikšmę taške x = 1.
Sprendimas:
h(x) = (x + 1)2.
h(1) = (1 + 1)2 = 4
Atsakymas: 4
16.2. Išspręskite lygtį g( f (x)) = 2.
Sprendimas:
g( f (x)) = x2 + 1;
x^2+1 =
2
2
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x^2+1 = 2$$x^{2}+1$$ = $$2$$
x^2 = 2-1$$x^{2}$$ = $$2-1$$
x^2 = 1$$x^{2}$$ = $$1$$
saknis( x^2) = saknis(1)$$\sqrt {x^{2}}$$ = $$\sqrt {1}$$
x^2) = saknis(1)$$\sqrt {x^{2}}$$ = $$\sqrt {1}$$x = saknis(1)$$x$$ = $$\sqrt {1}$$
1)$$x$$ = $$\sqrt {1}$$x = 1$$x$$ = $$1$$
saknis( x^2) = -saknis(1)$$\sqrt {x^{2}}$$ = $$-\sqrt {1}$$
x^2) = -saknis(1)$$\sqrt {x^{2}}$$ = $$-\sqrt {1}$$x = -saknis(1)$$x$$ = $$-\sqrt {1}$$
1)$$x$$ = $$-\sqrt {1}$$x = -1$$x$$ = $$-1$$
Atsakymas: x = - 1 ir x = 1