Question

The graph of a function increases twice as much over each subsequent equally sized interval. Which of the following could be the parent function of the graphed function?

Answer 1

I hope this helps you





square root of (4x+41)=x+5



4x+41>=0



x >= -10.25



(square root of4x+41)^2=(x+5)^2




4x+41=x^2+10x+25



x^2+6x-16 =0



x +8



x -2



(x+8)(x-2)=0




x= -8



x= 2 extraneous

Answer 2

Answer:

The correct option is 1.

Step-by-step explanation:

The given equation is

$\sqrt{4x+41}=x+5$

Taking square on both the sides.

$4x+41=(x+5)^2$

$4x+41=x^2+10x+25$              $[\because (a+b)^2=a^2+2ab+b^2]$

$0=x^2+10x+25-4x-41$

$0=x^2+6x-16$

$0=x^2+8x-2x-16$

$0=x(x+8)-2(x+8)$

$0=(x+8)(x-2)$

$x=2,-8$

Check the equation by x=2.

$\sqrt{4(2)+41}=2+5$

$\sqrt{49}=7$

$7=7$

LHS=RHS, therefore x=2 is not an extraneous solution.

Check the equation by x=-8.

$\sqrt{4(-8)+41}=-8+5$

$\sqrt{9}=-3$

$3=-3$

LHS≠RHS, therefore x=-8 is an extraneous solution.

Therefore option 1 is correct.