Given:
[tex]f(x)=(\frac{1}{4})^{-x}[/tex]f(x) is reflected about the y-axis and compressed vertically by a factor of 1/3.
Required:
We need to find the new function g(x).
Explanation:
The reflection of the function y=f(x) about y-axis is y=f(-x).
To reflect the given function f(x) about y-axis:
Replace x =-x in the given function f(x).
[tex]f(-x)=(\frac{1}{4})^{-(-x)}[/tex][tex]f(-x)=(\frac{1}{4})^x[/tex]Multiply both sides by 1/3 to get the function compressed vertically by a factor of 1/3.
[tex]\frac{1}{3}f(-x)=\frac{1}{3}(\frac{1}{4})^x[/tex]The new function is
[tex]g(x)=\frac{1}{3}(\frac{1}{4})^x[/tex]Final answer:
[tex]g(x)=\frac{1}{3}\times(\frac{1}{4})^x[/tex]
