Question

watch the video and then solve the problem given below.
click here to watch the video.
evaluate the function ( f(x) = x^2 + 7x - 4 ) at the given values of the independent variable and simplify.
(\boldsymbol{\text{a. } f(-3)}) (\boldsymbol{\text{b. } f(x + 9)}) (\boldsymbol{\text{c. } f(-x)})
(\boldsymbol{\text{a. } f(-3) = square}) (simplify your answer.)

Explanation:

Step1: Substitute $x=-3$ into $f(x)$

$f(-3) = (-3)^2 + 7(-3) - 4$

Step2: Calculate each term

$(-3)^2=9$, $7(-3)=-21$
$f(-3) = 9 - 21 - 4$

Step3: Simplify the expression

$f(-3) = 9 - 25$

Step4: Compute final value for part a

$f(-3) = -16$

Step1: Substitute $x=x+9$ into $f(x)$

$f(x+9) = (x+9)^2 + 7(x+9) - 4$

Step2: Expand squared and linear terms

$(x+9)^2 = x^2 + 18x + 81$, $7(x+9)=7x+63$
$f(x+9) = x^2 + 18x + 81 + 7x + 63 - 4$

Step3: Combine like terms

$f(x+9) = x^2 + (18x+7x) + (81+63-4)$

Step4: Simplify for part b

$f(x+9) = x^2 + 25x + 140$

Step1: Substitute $x=-x$ into $f(x)$

$f(-x) = (-x)^2 + 7(-x) - 4$

Step2: Simplify each term

$(-x)^2=x^2$, $7(-x)=-7x$

Step3: Final simplification for part c

$f(-x) = x^2 - 7x - 4$

Answer:

a. $\boldsymbol{-16}$
b. $\boldsymbol{x^2 + 25x + 140}$
c. $\boldsymbol{x^2 - 7x - 4}$