Question

If f (x) = x +2x+3,then find f (x+h)-f (x)/h (h not equal to 0).

Answer 1

Answer:

f (x) = x +2x+3

Put x=x+h

Where h is the change in x

f(x+h) =(x+h) +2(x+h) + 3

To find f(x+h) - f(x)/h

Put f(x) and f(x+h)

[(x+h) +2(x+h)+3]-(x+2x+3)/h

[x+h+2x+2h+3-x-2x-3]/h

[h+2h]/h

3h/h

3 is the answer

Answer 2

Answer:

Step-by-step explanation:

I assume the function f(x) is quadratic polynomial. Then, to find "h" we have to convert function into complete square form y = a(x - h)² + k, where

h = - $\frac{b}{2a}$  and k = (4ac - b²) / 4a

f(x) = x² + 2x + 3 = (x² + 2x + 1) - 1 + 3 = (x + 1)² + 2

f(x) = (x + 1)² + 2

Thus, coordinates of vertex are (- 1, 2) and h = - 1

f(x+h) - f(x) / h

f(x - 1) = (x - 1)² + 2(x - 1) + 3 = x² - 2x + 1 + 2x - 2 + 3 = x² + 2

$\frac{f(x)}{h}$ = (x² + 2x + 3) / (- 1) = - (x² + 2x + 3)

f(x - 1) - $\frac{f(x)}{-1}$ = x² + 2 - [- (x² + 2x + 3)] = x² + 2 + x² + 2x + 3 = 2x² + 2x + 5

f(x - 1) - $\frac{f(x)}{-1}$ = 2x² + 2x + 5