Exponential Functions Question

Question

A function f(x) has been transformed to g(x)=-3f(2x+4)+1. If f(x)=1/x, write the new equation of g(x) in proper form.

Answer 1

f(x) = 1/x replace x with 2x+4

f(2x+4) = 1/(2x+4)

3f(2x+4) = 3/(2x+4)

3f(2x+4)+ 1 = 3/(2x+4) + 1= (3+2x+4)/(2x+4) = (2x+7)/(2x+4)

g(x) = (2x+7)/(2x+4)