Diketahui fungsi f(x)=2x,g(x)=x² dan h(x)=3-x .tunjukan bahwa (f o (goh)) (x)=((f og)oh)(x)

[tex]f\left(x\right) & =2x\\ g\left(x\right) & =x^{2}\\ h\left(x\right) & =3-x[/tex]

[tex]\left(\left(f\circ g\right)\circ h\right)\left(x\right) & =\left(f\circ g\right)\left(h\left(x\right)\right)\\ \text{\hspace{23mm}} & =\left(f\circ g\right)\left(3-x\right)\\\text{\hspace{23mm}} & =f\left(g\left(3-x\right)\right)\\\text{\hspace{23mm}} & =f\left(\left(3-x\right)^{2}\right)\\\text{\hspace{23mm}} & =2\left(3-x\right)^{2}\\\text{\hspace{23mm}} & =2\left(x^{2}-6x+9\right)\\\text{\hspace{23mm}} & =2x^{2}-12x+18[/tex]

[tex]\left(f\circ\left(g\circ h\right)\right)\left(x\right) & =f\left(\left(g\circ h\right)\left(x\right)\right)\\\text{\hspace{23mm}} & =f\left(g\left(h\left(x\right)\right)\right)\\\text{\hspace{23mm}} & =f\left(g\left(3-x\right)\right)\\\text{\hspace{23mm}} & =f\left(\left(3-x\right)^{2}\right)\\\text{\hspace{23mm}} & =2\left(3-x\right)^{2}\\\text{\hspace{23mm}} & =2\left(x^{2}-6x+9\right)\\\text{\hspace{23mm}} & =2x^{2}-12x+18[/tex]