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I DID ONE WHO CAN HELP WITH REST

I DID ONE WHO CAN HELP WITH REST-example-1
User CermakM
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  • (f°g)(x) = x² + 20x + 80
  • (gof)(x) = x² + x + 8
  • (fof)(x) = x⁴ + 4x³ + 13x² + 4x + 1
  • (g°g)(x) = x + 16

These calculations show how the order of operations within composite functions affects the final result.

Given functions f(x) = x²+x and g(x) = x + 8, let's evaluate the composite functions:

1. (f°g)(x):

This means we evaluate g(x) first, then plug the result into f(x). So, (f°g)(x) = f(g(x)) = f(x+8) = (x+8)² + (x+8) = x² + 20x + 80.

2. (gof)(x):

Similarly, we evaluate f(x) first, then plug the result into g(x). So, (gof)(x) = g(f(x)) = g(x²+x) = (x²+x) + 8 = x² + x + 8.

3. (fof)(x):

This involves nesting f within itself. We evaluate f(x) twice. So, (fof)(x) = f(f(x)) = f(x²+x) = ((x²+x)² + (x²+x)) = x⁴ + 4x³ + 13x² + 4x + 1.

4. (g°g)(x):

Similar to (fof)(x), we evaluate g(x) twice. So, (g°g)(x) = g(g(x)) = g(x+8) = (x+8) + 8 = x + 16.

User Joyson
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