Find and simplify the following

Question

Let f(x) = 5x^2 + 5x-3. Find and simplify the following. f(3/a)

Let f(x) = 5x^2 + 5x-7. Find and simplify the following. f(a + h)

Answer 1

1)

 f(x)  =  5x^2 + 5x-3

Substitute x = 3/a in f(x)

 f(3/a)  =  5(3/a)^2 + 5(3/a) - 3

           =  5(9/a^2) + 15/a - 3  

           =  45/a^2 + 15/a - 3  

 f(3/a)  =  (45 + 15a - 3a^2 ) / a^2

b)

f(x) = 5x^2 + 5x - 7

Substitute x = a + h in f(x)

f(a + h)  =  5(a + h)^2 + 5(a + h) - 7

             =  5(a^2 + h^2 + 2ah) + 5a + 5h - 7 

             =  5a^2 + 5h^2 + 10ah + 5a + 5h - 7 

f(a + h)  =  5a^2 + 5h^2 + 10ah + 5a + 5h - 7 

Answer :

a)  f(3/a)  =  (45 + 15a - 3a^2 ) / a^2

b)  f(a + h)  =  5a^2 + 5h^2 + 10ah + 5a + 5h - 7