Question

Find the following expression: If f(x)=ax+bx2f(x)=ax+bx2, determine f(x+a)f(x+a) by substituting and simplifying.

A) f(x+a)=a(x+a)+b(x+a)²
B) f(x+a)=ax+bx²+a+b
C) f(x+a)=a(x+a)+b(x²+a²)
D) f(x+a)=ax²+bxt^4

Answer 1

To find f(x+a) when f(x) is given as ax + bx², we must substitute x with x+a and simplify. The correct expression for f(x+a) involves expanding the substitution and simplifying to get f(x+a) = f(x) + a + 2abx + ba². Therefore the Correct Answer is Option.A.

Step-by-step explanation:

The question asks for the expression for f(x+a) given that f(x) = ax + bx². To find f(x+a), we substitute x with x+a in the function.

The substitution gives us:

f(x+a) = a(x+a) + b(x+a)²
= ax + aa + b(x² + 2ax + a²)
= ax + a² + bx² + 2abx + ba²

Simplifying this expression:

f(x+a) = ax + a² + bx² + 2abx + ba²
= ax + a + bx² + 2abx + ba² (since a² = a)

We group like terms together:

f(x+a) = (ax + bx²) + (a + 2abx + ba²)
Since we know that ax + bx² is equal to f(x), we can write:
f(x+a) = f(x) + a + 2abx + ba²

Therefore, the correct option is not listed above directly, but the closest option, if corrected for typos, would be:

• A) f(x+a) = a(x+a) + b(x+a)²