Question

F(x) = x^2 what is g(x)?

Answer 1

Answer IN THE PICTURE BELOW

G(X)=(1/4X)^2

Answer 2

`g(x)=((1)/(4)x)^2`

Explanation:

The given functions are;

`f(x)=x^2`

The function g(x) is a vertical stretch of f(x) by a factor of 'a' units, therefore we can write g(x) in terms of f(x).

This implies that;

`g(x)=a\bullet f(x)`

`\implies g(x)=a\bullet x^2`

The graph of g(x) passes through (4,1).

`\implies g(4)=1`

`\implies a(4^2)=1`

`\implies 16a=1`

`\implies a=(1)/(16)`

This implies that;

`\implies g(x)=(1)/(16)x^2`

Or

`g(x)=((1)/(4)x)^2`