Question

Suppose that the functions and g are defined for all real numbers x as follows f(x) = 3x + 5; g(x) = x + 4 Write the expressions for (f + g)(x) and (fg)(x) and evaluate (f - g)(1) .

Answer 1

(f + g)(x) = 4x + 9

(fg)(x) = 3x² + 17x + 20

(f - g)(x) = 2x + 1

Step-by-step explanation:

We know that

f(x) = 3x + 5

g(x) = x + 4

Then, we can find (f + g)(x) as follows

(f + g)(x) = f(x) + g(x)

(f + g)(x) = (3x + 5) + (x + 4)

(f + g)(x) = 3x + 5 + x + 4

(f + g)(x) = 4x + 9

In the same way, we can calculate (fg)(x) and (f - g)(x) as follows

(fg)(x) = f(x)g(x)

(fg)(x) = (3x + 5)(x + 4)

(fg)(x) = 3x(x) + 3x(4) + 5(x) + 5(4)

(fg)(x) = 3x² + 12x + 5x + 20

(fg)(x) = 3x² + 17x + 20

(f - g)(x) = f(x) - g(x)

(f - g)(x) = (3x + 5) - (x + 4)

(f - g)(x) = 3x + 5 - x - 4

(f - g)(x) = 2x + 1

Therefore, the answers are

(f + g)(x) = 4x + 9

(fg)(x) = 3x² + 17x + 20

(f - g)(x) = 2x + 1