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two functions f and g are defined on a suitable domain by f(x)=x^(2)-1 and g(x)=x^(2)+2 . a) find a formula for f(g(x)) . b) factorise

Question

Two functions f and g are defined on a suitable domain by f(x)=x^(2)-1 and g(x)=x^(2)+2 . a) Find a formula for f(g(x)) . b) Factorise f(g(x)) .

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Seth Elite · Tutor for 8 years

Answer

a) \(f(g(x)) = x^4 + 4x^2 + 3\)b) \(f(g(x)) = (x^2 + 1)(x^2 + 3)\)

Explanation

1. To find a formula for \(f(g(x))\), we need to substitute \(g(x)\) into \(f(x)\). Given \(f(x) = x^2 - 1\) and \(g(x) = x^2 + 2\), we get: Expanding the expression, we obtain: 2. To factorise \(f(g(x))\), we factorise the polynomial . The factorisation is: