Question

If f(x)=x³-1 and g(x)=x²

find (gof) ( x) and (fog) (x)
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Answer 1

(x²)³ - 1 = x^6 - 1

Explanation:

To find (gof)(x), we first need to evaluate g(x), which is x², and then use the result as input to f(x), giving us f(g(x)).

So, we have:

g(x) = x²

f(g(x)) = f(x²) = (x²)³ - 1 = x^6 - 1

Therefore, (gof)(x) = g(f(x)) = (f(x))² = (x³ - 1)² = x^6 - 2x^3 + 1.

To find (fog)(x), we first need to evaluate f(x), which is x³ - 1, and then use the result as input to g(x), giving us g(f(x)).

So, we have:

f(x) = x³ - 1

g(f(x)) = g(x³ - 1) = (x³ - 1)² = x^6 - 2x^3 + 1

Therefore, (fog)(x) = f(g(x)) = (x²)³ - 1 = x^6 - 1.