Question

f(x) = x² + 5, f(x + 4)
a. x² + 16
b. x² + 9
c. x² + 8x + 21
d. x² + 8x + 16

Explanation:

Step1: Substitute \( x+4 \) into \( f(x) \)

Given \( f(x) = x^2 + 5 \), to find \( f(x + 4) \), we replace every \( x \) in the function with \( x + 4 \). So we get \( f(x + 4)=(x + 4)^2+5 \).

Step2: Expand \( (x + 4)^2 \)

Using the formula \( (a + b)^2=a^2+2ab + b^2 \), where \( a = x \) and \( b = 4 \), we have \( (x + 4)^2=x^2+8x + 16 \).

Step3: Simplify the expression

Substitute the expanded form back into \( f(x + 4) \): \( f(x + 4)=x^2+8x + 16+5 \). Combine like terms: \( x^2+8x+(16 + 5)=x^2+8x + 21 \).

Answer:

C. \( x^2 + 8x + 21 \)