Question

If f(x)=x^2+3x+5, what is f(3+h)

A.(x^2+3x+5)(3+h)
B.h^2+9h+23
C.(3+h)^2+8+h
D.h^2+h+23

Answer 1

F(x) = x^2 +3x + 5. For f( 3+h), put x = 3+h. F( 3+h)= (3+h) ^2 + 3 (3+h) +5 = 9 +h^2 + 6h + 9 + 3h + 5 = h^2 + 9h + 23. B is the correct option.

Answer 2

The value of the f (3 +h) is h² + 9h + 23 .

Option (B) is correct.

Explanation:

As the function given in the question be

f(x)= x² + 3x + 5

Now

f(3 +h )= (3 +h )²+3(3 + h)+5

Now by using the formula

(a + b)² = a² + b² + 2ab

f(3 +h )= 3² + h² + 2 × 3 × h +3 × 3 + 3 ×h +5

f(3 +h )= 9 + h² + 6h + 9 + 3h +5

f(3 +h )= h² + 9 + 9 + 5 + 3h + 6h

f(3 +h )= h² + 9h + 23

Therefore the value of the f (3 +h) is h² + 9h + 23 .

Option (B) is correct.