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

The composition was done in the incorrect order.
The negative sign for f(x) was not included in the calculation.
The coefficient of f(x) was squared incorrectly.
The coefficients should be multiplied and then squared.

Answer 1

f(g(x)) means you take the g function and put it into x in the f function. He took the function and put it into the g, which was the incorrect order. He should have had this:
`f(g(x))=-4(5x^2)`

Answer 2

Option 1 - The composition was done in the incorrect order.

Explanation:

Given :
`f(x)=-4x` and
`g(x)=5x^2` . Andrew finds the composition [f o g](x) as shown below.

`[f o g](x)= 5(-4x)^2 = 5(16x^2) = 80x^2`

To find : What error did Andrew make?

Solution :

We have given two functions
`f(x)=-4x` and
`g(x)=5x^2`

Now, we find [f o g](x) i.e, substitute the value of g in f(x)

`[f o g](x)=f(g(x))=f(5x^2)`

`[f o g](x)=-4(5x^2)`

`[f o g](x)=-20x^2`

Exact solution is
`[f o g](x)=-20x^2`.

Andrew mistake is that he finds [g o f](x) i.e, he take the composition in incorrect order.

Therefore, Option 1 is correct.

The composition was done in the incorrect order.