Let f(x) = x2 and g(x) = 2x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is
Explanation:
We have to calculate f [f(g(x)) + g(f(x))]
First we need to calculate f(g(x)) and g(f(x))
At x = 1, f[g(x)] = f[g(1)] Now g(1) = 21 = 2 f[g(1)] = f(2) = 4 At x = 1, g[f(x)] = g[f(1)] Now f(1) = 1 and g[f(1)] = g(1) = 21 = 2 Now at x = 1 f [f(g(x)) + g(f(x))] = f(4 + 2) = f(6) = 36
Hence, option (c).
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