Methods2026 NHT Exam 2 Section A · Q15CAS active1 mark

Average value under transformations

Consider a continuous function $f : R \to R$ , which has an average value of 2 over the interval $[-1, 1]$ .

Let $g : R \to R$ , $g(x) = mf(nx) + c$ , where $m$ , $n$ and $c$ are positive real numbers.

Which one of the following must be true for all possible values of $m$ , $n$ and $c$ ?

1 mark

g

has an average value of

2m

over the interval

[-n, n]

g

has an average value of

2m

over the interval

\left[-\frac{1}{n}, \frac{1}{n}\right]

g

has an average value of

2m + c

over the interval

[-n, n]

g

has an average value of

2m + c

over the interval

\left[-\frac{1}{n}, \frac{1}{n}\right]

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