Given.....

Question

f(x)= x-7 if x > 0

        2x if x ≤ 0

 

        and

 

g(x)= f(3x). what is g(x)?

 

 

 

 

A) g(x)=  x-4 if x > 0

              2x+3 if x ≤ 0

 

 

B) g(x)= 3x-21 if x > 0

              6x if x ≤ 0

 

C) g(x)= 3x-7 if x > 0

              6x if x ≤ 0

 

D) g(x)= 3x if x > 0

              3x if x ≤ 0

Answer 1

to find f(3x), simply replace all x with 3x in the function definition:
f(3x) = (3x)-7 if (3x)>0
2(3x) if (3x) ≤ 0

3x > 0 implies that x > 0, and 3x ≤ 0 implies that x ≤ 0.

We then have g(x) = f(3x)
= 3x - 7 if x>0
6x if x ≤ 0