The expression to the correct combined function is:
(f+g)x = x² + 6x + 9
(f-g)x = x² + 4x + 3
(f.g)x = x³ + 8x² + 21x + 18
(f/g)x = x + 2
The sum, difference, product and quotient of two functions f and g are defined as follows.
Sum → (f + g)(x) = f(x) + g(x)
Difference → (f - g)(x) = f(x) - g(x)
Product → (f * g)(x) = f(x) * g(x)
Quotient → (f / g)(x) = f(x) / g(x)
As we have to find all the arithmetic combinations:
1. Sum: (f + g)(x) = f(x) + g(x)
f(x) = x² + 5x + 6 and g(x) = x + 3
(f + g)(x) = x² + 5x + 3 + x + 3
(f + g)(x) = x² + 6x + 6
2. Difference: (f - g)(x) = f(x) - g(x)
f(x) = x² + 5x + 6 and g(x) = x + 3
(f - g)(x) = x² + 5x + 6 - (x + 3)
(f - g)(x) = x² + 4x + 3
3. Product: (f * g)(x) = f(x) * g(x)
f(x) = x² + 5x + 6 and g(x) = x + 3
(f * g)(x) = (x² + 5x + 6) . (x + 3)
(f * g)(x) = x³ + 8x² + 21x + 18
4. Quotient: (f / g)(x) = f(x) / g(x)
f(x) = x² + 5x + 6 and g(x) = x + 3
(f / g)(x) = (x² + 5x + 6 ) / (x + 3)
(f / g)(x) = x + 2
Hence,
The expression to the correct combined function is
(f+g)x = x² + 6x + 9
(f-g)x = x² + 4x + 3
(f.g)x = x³ + 8x² + 21x + 18
(f/g)x = x + 2
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Disclaimer: The question given was incomplete on the portal. Here is the complete question.
Question: Drag each expression to the correct location on the table. Not all expressions will be used.
Consider functions f and g.
f(x)=x^2+5x +6
g(x)=x+3
Match each expression to the correct combined function.
See the attached image.
