Question

Fie f(x)=2x+3, 4. Calculati: g(x) = 3x+2. a) (fog) (1) = b) (gof) (2) = c) (fog)(x) = X1 x2​

Answer 1

Explicație pas cu pas:

$f(x)=2x+3; \: g(x) = 3x+2$

$(fog)(x) = f(g(x)) = 2 \times g(x) + 3 = 2(3x + 2) + 3 = 6x + 4 + 3 = 6x + 7$

$(gof)(x) = g(f(x)) = 3 \times f(x) + 2 = 3(2x + 3) + 2 = 6x + 9 + 2 = 6x + 11$

a)

$(fog)(1) = 6 \times 1 + 7 = 6 + 7 = 13$

sau:

g(1) = 3×1 + 2 = 3 + 2 = 5

f(g(1)) = f(5) = 2×5 + 3 = 10 + 3 = 13

b)

$(gof)(2) = 6 \times 2 + 11 = 12 + 11 = 23$

sau:

f(2) = 2×2 + 3 = 4 + 3 = 7

g(f(2)) = g(7) = 3×7 + 2 = 21 + 2 = 23