Question

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

Answer 1

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

Answer 2

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.

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.