Let f (x) = - x2 + 3x + 1 and g (x) = 2x. Look at the composition shown. What is the error in the student's work? f (g (x)) = - (2x) 2 + 3x + 1 = - 4x2 + 3x + 1

The error he did was that in place of 3 (2x) he wrote 3x

i. e. the error was in the second term of the expression.

Step-by-step explanation:

We are given that:

f (x) = - x² + 3x + 1 and g (x) = 2x

f (g (x)) = f (2x)

= - (2x) ²+3 (2x) + 1

= - 4x²+6x+1

But, student wrote it as:

f (g (x)) = - (2x) ² + 3x + 1 = - 4x² + 3x + 1

On comparing our work with the students work, we see that

The error he did was that in place of 3 (2x) he wrote 3x

i. e. the error was in the second term of the expression.

in term 3x, the correct is 3 (2x)