Question

g(x)=2/x+1 ,h(x)=(x+2)²-5 Find the equation hg(x)=11

Answer 1

Answer:

g(x)= 2/x+1

h(x)=$(x+2)^{2}$-5= $x^{2}$+4x+4

hg(x)=(2/x+1)($x^{2}$+4x+4)

hg(x)= 2x+8+8/x+$x^{2}$+4x+4)

hg(x)=$x^{2}$+6x+8/x+12= $x^{2}$+$\frac{6xsqrd+8}{x}$+12

as, hg(x)=11

$x^{2}$+$\frac{6xsqrd+8}{x}$+12=11

$x^{3}$+6$x^{2}$+12x+8=11

$x^{3}$+6$x^{2}$+12x+8-11=0

$x^{3}$+6$x^{2}$+12x-3=0