Question

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

Answer 1

`\large\boxed{C.\ a^2+2ah+h^2+3a+3h+5}`

Explanation:

`f(x)=x^2+3x+5\\\\f(a+h)\to\text{put}\ x=a+h\ \text{to the equation of a function:}\\\\f(a+h)=(a+h)^2+3(a+h)+5\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\ \text{and the distributive property}\\\\f(a+h)=a^2+2ah+h^2+3a+3h+5`

Answer 2

Choice B is correct answer.

Explanation:

From question statement , we observe that

A function is given.

f(x) = x²+3x+5

We have to find f(a+h).

f(a+h) = ?

Given function depends on x. We have to find function that depends on a+h.

Putting x = a+h in given function , we have

f(a+h) = (a+h)²+3(a+h)+5(a+h) which is the answer.