1) For f(x) = 2x + 3 and g(x) = -x2 + 1, find the composite function defined by (f o g)(x) a) - 2 x + 5 b) - 2 x2 + 5 c) -2 x + 5 d) - 2 x2 2) Given the functions f (x) = x2 + 6 and g (x) = 2x – 1, find (f ∘ g) (x). a) 4x + 7 b) 4x2 – 4x  c) 4x2 – 4x + 7 d) 4x 3) Given the functions g (x) = 2x – 1 and f (x) = x2 + 6, find (g ∘ f) (x). a) 2x + 11 b) x2 + 11 c) 2x2 d) 2x2 + 11 4) Given f (x) = 2x + 3, find (f ∘ f) (x). a) 4x + 9 b) 4x c) 4x - 9 d) x + 9 5) Find f [g (5)] given that, f (x) = 4x + 3 and g (x) = x – 2. a) 11 b) 15 c) 10 d) 20 6) Given that g(x) = x - 5, find g-1(2) a) 1 b) 3 c) 5 d) 7 7) If g(x) = 9x + 2, then what is g(g(x))? a) 81x + 20 b) 81x - 20 c) 81x + 2 d) 8x + 20 8) For the given two functions f(x) = kx - 4 and g(x) = kx + 6, if the two composite functions f(g(x)) and g(f(x)) are equal for all x, find k. a) 2 b) 1 c) 3 d) 4 9) Find (g ∘ f) (x) if, f(x) = 6 x² and g(x) = 14x + 4 a) 84 x² + 4 b) 8x + 4 c) 84 x² d) 84 x² - 4 10) Calculate (f ∘ g) (x) using f(x) = 2x + 3 and g(x) = -x2 + 1, a) 2 x2 + 5 b) – 2 x2 + 5 c) – 2 x2 -5 d) – 2 x2

RELATION AND FUNCTION: Simplify composite functions

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