Question

evaluate the function $f(x) = x^2 + 8x + 7$ at the given values of the independent variable and si
a. $f(8)$ b. $f(x + 5)$ c. $f(-x)$
a. $f(8) = 135$ (simplify your answer.)
b. $f(x + 5) = \square$ (simplify your answer.)

Explanation:

Step1: Substitute \( x + 5 \) into \( f(x) \)

We have \( f(x)=x^{2}+8x + 7 \), so substitute \( x\) with \(x + 5\):
\(f(x + 5)=(x + 5)^{2}+8(x + 5)+7\)

Step2: Expand the expressions

First, expand \((x + 5)^{2}\) using the formula \((a + b)^{2}=a^{2}+2ab + b^{2}\), where \(a=x\) and \(b = 5\):
\((x + 5)^{2}=x^{2}+10x+25\)
Then expand \(8(x + 5)\):
\(8(x + 5)=8x+40\)
Now substitute these back into \(f(x + 5)\):
\(f(x + 5)=x^{2}+10x + 25+8x+40 + 7\)

Step3: Combine like terms

Combine the \(x\) - terms and the constant terms:
For the \(x\) - terms: \(10x+8x = 18x\)
For the constant terms: \(25 + 40+7=72\)
So \(f(x + 5)=x^{2}+18x + 72\)

Answer:

\(x^{2}+18x + 72\)