Question

evaluate the function $f(x)=x^2 + 8x + 7$ at the given values of the independent variable and \
ewline a. $f(8)$ \quad b. $f(x + 5)$ \quad c. $f(-x)$ \
ewline \
ewline a. $f(8)= 135$ (simplify your answer.) \
ewline \
ewline b. $f(x + 5)= x^2 + 18x + 72$ (simplify your answer.) \
ewline \
ewline c. $f(-x)=\square$ (simplify your answer.)

Explanation:

Step1: Substitute -x into f(x)

To evaluate \( f(-x) \), we substitute \( -x \) for \( x \) in the function \( f(x) = x^2 + 8x + 7 \). So we get \( f(-x) = (-x)^2 + 8(-x) + 7 \).

Step2: Simplify each term

First, simplify \( (-x)^2 \). Remember that squaring a negative number gives a positive result, so \( (-x)^2 = x^2 \). Then, simplify \( 8(-x) \), which is \( -8x \). So now the expression becomes \( x^2 - 8x + 7 \).

Answer:

\( x^2 - 8x + 7 \)