Question

Желательно хотя-бы поверхностные объяснения :(

Answer 1

1) $y = f(x + 1) = -3x - 2$

2) $y = g \left(\dfrac{1}{x} \right) = \dfrac{1}{x^{2} } - 1$

3) $y = f(g(x)) = 4 - 3x^{2}$

4) $y = g(f(x)) = 9x^{2} - 6x$

5) $y = f(f(x)) = 9x - 2$

6) $y = g(g(x)) = x^{4} - 3x^{2} + 1$

Объяснение:

$f(x) = 1 - 3x$

$g(x) = x^{2} - 1$

1) $y = f(x + 1) = 1 - 3(x + 1) = 1 -3x -3 = -3x - 2$

2) $y = g \left(\dfrac{1}{x} \right) = \left(\dfrac{1}{x} \right)^{2} - 1 = \dfrac{1}{x^{2} } - 1$

3) $y = f(g(x)) = 1 - 3(x^{2} - 1) = 1 - 3x^{2} + 3 = 4 - 3x^{2}$

4) $y = g(f(x)) = (1 - 3x)^{2} - 1 = 1 - 6x + 9x^{2} - 1 = 9x^{2} - 6x$

5) $y = f(f(x)) = 1 - 3(1 - 3x) = 1 -3 + 9x = 9x - 2$

6) $y = g(g(x)) = (x^{2} - 1) - x^{2} = x^{4} - 2x^{2} + 1 - x^{2} = x^{4} - 3x^{2} + 1$