TMUA 2018 Paper 2 Q11 — Worked Solution

P2·Functions, Transformations & Graphs, Logic & Quantifiers·7.0Official · 2018 · Q11

exponential-line-intersectioncounterexamplenecessary-vs-sufficientif-only-if

Consider the equation

2^{x} = m x + c

, where

m

and

c

are real constants.Which of the following statements is/are true?

The equation has a negative real solution only if

c > 1

The equation has two distinct real solutions if

c > 1

III

The equation has two distinct positive real solutions if and only if

c \leq 1

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