Question a. If g(x) is any (nonzero) odd function of x, determine whether the following functions, f(x) = 42 sin(g(x)), f(x)= 5x³g(x), are even, odd functions of x, or none of these. b. Find the values of a and b such that the function. I f(x) = (g(x) + 1)² h(x) = 3ae* + 12e¯* + b is an even function of x and its curve, y = h(x), passes through the point (0,17). Remember to show full working.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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a. If g(x) is any (nonzero) odd function of x, determine whether the following
functions,
f(x) = (g(x) + 1)²
f(x) = 42 sin(g(x)), f(x) = 5x³ g(x),
are even, odd functions of x, or none of these.
b. Find the values of a and b such that the function.
I
h(x) = 3ae* + 12e¯* + b
is an even function of x and its curve, y = h(x), passes through the point (0,17).
Remember to show full working.
Transcribed Image Text:Question a. If g(x) is any (nonzero) odd function of x, determine whether the following functions, f(x) = (g(x) + 1)² f(x) = 42 sin(g(x)), f(x) = 5x³ g(x), are even, odd functions of x, or none of these. b. Find the values of a and b such that the function. I h(x) = 3ae* + 12e¯* + b is an even function of x and its curve, y = h(x), passes through the point (0,17). Remember to show full working.
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