Question

Let f(x) = –4x and g(x) = 5x2. Andrew finds the composition [f o g](x) as shown below. What error did Andrew make? = 5(–4x)2 = 5(16x2) = 80x2

Answer 1

He squared 4x instead of adding exponents of x and multiplying -4 by 5.

Explanation:

When multiplying to exponents with the same base you must add the exponents. Andrew multiplied the two functions and took 4x and squared it to get 4x² which is wrong. The correct solution is:

`=-4\cdot(x)\cdot(5)\cdot(x^2)`

`=-20\cdot(x)^(1+2)=-20\cdot(x^3)`

Answer 2

We are given
(x) = –4x and g(x) = 5x²
The composition of f with g should be done this way:
[f o g](x) = f [ g(x) ]
= f ( 5x² )
= -4 (5x²)
- 20 x²