Question

F(x) = x ^ 2 . What is g(x) ?

Answer 1

Given:

The function is:

$f(x)=x^2$

The graphs of functions $f(x)$ and $g(x)$.

To find:

The function $g(x)$.

Solution:

We have,

$f(x)=x^2$

The function $f(x)$ is vertically compresses to get the graph of the function $g(x)$. So, the function $g(x)$ is:

$g(x)=kf(x)$

$g(x)=kx^2$               ...(i)

From the given graph it is clear that the graph of the function $g(x)$ passes through the point (3,3). So, putting $x=3$ and $g(x)=3$ in the above function, we get

$3=k(3)^2$

$3=9k$

$\dfrac{3}{9}=k$

$\dfrac{1}{3}=k$

Putting $k=\dfrac{1}{3}$ in (i), we get

$g(x)=\dfrac{1}{3}x^2$

Therefore, the correct option is D.