a. f(x) = x^{2} +1, g(x) = 2x

To find f[g(x)], put the value of g(x) for all x in f(x).

f[g(x)] = (2x)^{2} + 1 = 4x^{2} + 1

To find g[f(x)], put the value of f(x) for all x in g(x).

g[f(x)] = 2(x^{2} + 1) = 2x^{2} + 2

b. f(x) = sinx, g(x) = 1 – x^{2}

To find f[g(x)], put the value of g(x) for all x in f(x).

f[g(x)] = sin(1 – x^{2})

To find g[f(x)], put the value of f(x) for all x in g(x).

g[f(x)] = 1 – sin^{2}x = cos^{2}x

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