Question

question 6
score: 0 of 1 point
given function (f(x)=9x^{p}-10), which integer values of (p) in range (3,6) make the function one - to - one.
answer all values, separated by commas. example: 1, 2, 3.
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Explanation:

Step1: Recall one - to - one function condition

A function \(y = f(x)=ax^{n}+b\) is one - to - one if \(n\) is odd. We need to find when \(p\) in \(f(x)=9x^{p}-10\) makes the function one - to - one in the range \(p\in[3,6]\).

Step2: Check values of \(p\) in the range

The values of \(p\) in the range \([3,6]\) are \(p = 3,4,5,6\). For a polynomial function \(y = ax^{n}+b\), when \(n\) is odd, the function is one - to - one. Among \(3,4,5,6\), the odd values of \(p\) are \(3\) and \(5\).

Answer:

3, 5