Methods2025 NHT Exam 1 · Q7Tech-free7 marks

Quadratic roots, inverse and composite domain

Let $f: \R \to \R, f(x) = x^2 + bx - 6$ , where .

Find the values of $b$ for which the two solutions of $f(x) = 0$ have a difference of 5.

2 marks

Hints, answer checking and worked solutions come with a Season Pass.

b.i.

Let $b < 0$ .

Explain why an inverse function does not exist when $f$ is restricted to the domain $(0, \infty)$ .

1 mark

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b.ii.

Find a rule for the inverse function of $f$ when $f$ is restricted to the domain $(-\infty, 0)$ .

2 marks

Hints, answer checking and worked solutions come with a Season Pass.

Let $g$ be a function with maximal domain and the rule $g(x) = \log_e(-x - 2)$ .

Find the value of $b$ for which the maximal domain of the composite function $g \circ f$ is $(-2, 2)$ .

2 marks

Hints, answer checking and worked solutions come with a Season Pass.