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Can someone explain how to answer this composite function question (1 Viewer)

cheesynooby

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i think the best method for these kinds of questions is usually to just sub values in (almost always works, less room for mistakes)
but heres a perhaps less guess and check type approach
B is gone because of the change in gradient over a range that does not match the range of h(x) (if it was B we should see peaks lower in h(x))
(also B just looks pretty asymmetrical and ew)
we expect a peak at x = -1/2 (if wlog we let each tick mark be 1 unit)
that means the blue graph at x = -1/2 should be positive --> leading to a positive h(x) value since the f(x) is positive for positive inputs
so the only graph that satisfies this is C.
A and D would be the same graph but with a different phase since f(x) is the same and g(x) is only shifted horizontally (so basically we only have one option anyway: to test points)
 

cheesynooby

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(ok i feel like i didnt stress this enough but for these questions just save urself the hassle and test points/do a table of values it's just more efficient)
 

coolcat6778

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or just skip it completely. make an educated guess. mcq are designed like this to test ur elimination skills
 

lazystudentzzz

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you can see the function is ODD,

g(x) must be ODD as well since g(x) is the inside function

hence C
how do we tell from graphs if a function is odd or even? its just ab symmetry right?
symmetrical (reflected on y-axis) = even function
point symmetry (rotated on a point) = odd function
 

SS173

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odd ∘ odd = odd: The composition of two odd functions is odd.
even ∘ odd = even: The composition of an even function and an odd function is even.
odd ∘ even = even: The composition of an odd function and an even function is also even.
Any function composed with an even function is even.

The graph of h(x)is odd. So both f(x) and g(x) must be odd. option C is the only one satisfying this condition.
 

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