MAT1510 ASSIGNMENT 2 2026 – FULLY ANSWERED (DUE 18 JUNE 2026)

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MAT1510 Assignment 2 Memo | Due 18 June 2026. All questions fully answered. Question 1: 13 Marks
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give
an example that disproves the statement.
(1.1) If D(x) = (3)
√
x, where x ∈ R, then D(a+b) = D(a)+D(b).
(1.2) If s ̸= t, where s, t ∈ R and f is a function, then it follows that f (s) ̸= f (t). (2)
(1.3) If f and g are functions, then f (ag(x)) = g(f (ax)). (3)
(1.4) A vertical line that intersects the graph of a function is a tangent line. (2)
(1.5) If g is a many-to-one function, then an inverse function g−1 does not exist. (3)