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Relations and Functions | Composition of Functions

Let f: R→R be defined by f(x) = cos x and g: R→R be defined by g(x) = ex then f o g is –
If f(x) = 4x + 3, then what is f o f o f(-1) equal to?
If f(x) = ax + b and g(x) = cx + d such that f(g(x)) = g(f(x)), then which one of the following is correct?
H1(x) = 1 – x, 0 < x < 1          = 1, x ≥ 1          = 0, otherwise H2(x) = -H1(x) for all x H3(x) = H2 (-x) for all x H­4(x) = -H3(x) for all x How many of the following products are necessarily zero for every value of ‘x’? H1(x) * H3(x); H3(x) * H2(x); H1(x) * H2(x)
f : R → [0, ∞) and g : [0, ∞) → R is defined by f(x) = x2 and g(x) = √x. Which one of the following is not true? 
Let \(f:\left[ { - 6,\;6} \right] \to R\) be defined by f(x) = x2 – 3. Consider the following: 1. (f ∘ f ∘ f) (-1) = (f ∘ f ∘ f) (1) 2. (f ∘ f ∘ f) (-1) – 4 (f ∘ f ∘ f) (1) = (f ∘ f) (0) Which of the above is/are correct?
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