Question

If h(x)-(fog)(x) and h(x) = 4(x+1)*, find one possibility for 5 %) and g(x).f(x) = x +1O A.8(x) = 4x2O B. M(x)=(x+1)8(x)=4x2O c.f(x) = 4x2g(x) = x +1D.f(x) = 4x28(x)= (x+1)

Answer 1

It is given that h(x)=fog(x) and h(x)=4(x+1)^2.

So it follows:

$\text{fog(x)}=4(x+1)^2$

For option A, f(x)=x+1,g(x)=4x^2

So the value of fog(x) is given by:

$f(g(x))=g(x)+1=4x^2+1$

So A is incorrect.

For option B, f(x)=(x+1)^2,g(x)=4x^2

So the value of fog(x) is given by:

$f(g(x))=g(x)+1=(g(x)+1)^2=(4x^2+1)^2$

So B is incorrect.

For option C, f(x)=4x^2,g(x)=x+1

So the value of fog(x) is given by:

$f(g(x))=4\lbrack g(x)\rbrack^2=4(x+1)^2$

So C is correct.