minta tolong dong yang bisa!
Answer (1)
Penyelesaian1. a. [tex]((f \circ g)(x) = f(g(x)))[/tex][tex]f(g(x)) = f(2x+1) = (2x+1)^2 - 12(2x+1) + 10[/tex][tex]= 4x^2 + 4x + 1 - 24x - 12 + 10[/tex][tex]= 4x^2 - 20x - 1[/tex][tex](f \circ g)(x) = 4x^2 - 20x - 1[/tex]b. [tex]((g \circ f)(x) = g(f(x)))[/tex][tex]= 2x^2 - 24x + 20 + 1[/tex][tex]= 2x^2 - 24x + 21[/tex][tex](g \circ f)(x) = 2x^2 - 24x + 21[/tex]2. a.[tex]((f \circ g)(x) = f(g(x)))[/tex][tex]f(g(x)) = f(x^2 + 12x + 35) = (x^2 + 12x + 35) - 7[/tex][tex]= x^2 + 12x + 28[/tex][tex](f \circ g)(x) = x^2 + 12x + 28[/tex]b.[tex]((g \circ f)(x) = g(f(x)))[/tex][tex]g(f(x)) = g(x - 7)[/tex][tex]= (x - 7)^2 + 12(x - 7) + 35[/tex][tex]= x^2 - 14x + 49 + 12x - 84 + 35[/tex][tex]= x^2 - 2x + 0[/tex][tex]= x^2 - 2x[/tex][tex](g \circ f)(x) = x^2 - 2x[/tex]3. a. [tex]((f \circ g \circ h)(x) = f(g(h(x))))[/tex][tex]h(x) = x^2 - 2[/tex][tex]g(h(x)) = 2(x^2 - 2) + 4 = 2x^2 - 4 + 4[/tex][tex]= 2x^2[/tex][tex]f(g(h(x))) = f(2x^2) = -\frac12 (2x^2)[/tex][tex]= -x^2[/tex][tex](f \circ g \circ h)(x) = -x^2[/tex]b. [tex]((h \circ f \circ g)(x) = h(f(g(x))))[/tex][tex]g(x) = 2x + 4[/tex][tex]f(g(x)) = -\frac12 (2x + 4) = -x - 2[/tex][tex]h(f(g(x))) = (-x - 2)^2 - 2 = (x + 2)^2 - 2[/tex][tex]= x^2 + 4x + 4 - 2 = x^2 + 4x + 2[/tex][tex](h \circ f \circ g)(x) = x^2 + 4x + 2[/tex]c. [tex]((h \circ g \circ f)(-2)[/tex][tex]f(-2) = -\frac12 (-2) = 1[/tex][tex]g(1) = 2(1) + 4 = 6[/tex][tex]h(6) = 6^2 - 2[/tex][tex]= 36 - 2[/tex][tex]= 34[/tex][tex](h \circ g \circ f)(-2) = 34[/tex]d. [tex]((g \circ h \circ f)(0))[/tex][tex]f(0) = -\frac12(0) = 0[/tex][tex]h(0) = 0^2 - 2 = -2[/tex][tex]g(-2) = 2(-2) + 4[/tex][tex]= -4 + 4[/tex][tex]= 0[/tex][tex](g \circ h \circ f)(0) = 0[/tex]
