Question

F(x)=x2 what is g(x)?

Answer 1

g(x) = (1/4)x^2 . correct option C) .

Step-by-step explanation:

Here we have , $f(x)=x^2$  and we need to find g(x) from the graph . Let's find out:

We have ,  $f(x)=x^2$   . From the graph we can see that g(x) is passing through point (2,1 ) . Let's substitute this point in all of the four options !

A . g(x) = (1/4x)^2

Putting (2,1) in equation g(x) = (x/4)^2 , we get :

⇒ $g(2)= (\frac{2}{4} )^2$

⇒ $1\neq \frac{1}{4}$

Hence , wrong equation !

B . g(x) = 4x^2

Putting (2,1) in equation g(x) = 4x^2 , we get :

⇒ $g(2)=4(2)^2$

⇒ $1\neq 64$

Hence , wrong equation !

C . g(x) = (1/4)x^2

Putting (2,1) in equation g(x) = (1/4)x^2 , we get :

⇒ $g(2)= (\frac{1}{4} )2^2$

⇒ $1= 1$

Hence , right equation !

D . g(x) = (1/2)x^2

Putting (2,1) in equation g(x) = (1/2)x^2 , we get :

⇒ $g(2)= (\frac{1}{2} )2^2$

⇒ $1\neq 2$

Hence , wrong equation !

Therefore , g(x) = (1/4)x^2 . correct option C) .