Question

If f(x)=4x and g(x)=5x+1, then what is the rule for f(2g(x))? what is the rule for g(f(x)+1)?

Answer 1

Given

• 
  `f(x)=4x;`
• 
  `g(x)=5x+1.`

1. Find the rule for
`f(2g(x)):`

`f(2g(x))=f(2\cdot (5x+1))=f(10x+2)=4\cdot (10x+2)=40x+8.`

2. Find the rule for
`g(f(x)+1):`

`g(f(x)+1)=g(4x+1)=5\cdot (4x+1)+1=20x+5+1=20x+6.`

Answer:
`f(2g(x))=40x+8,`
`g(f(x)+1)=20x+6.`