Question

8-81. if $f(x)=x^2 + 7x - 9$, calculate the values in parts (a) through (c) below. homework help \\a. $f(-3)$ \\b. $f(t)$ \\c. $f(-3 + t)$

Explanation:

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

$f(-3) = (-3)^2 + 7(-3) - 9$

Step2: Compute each term

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

Step3: Simplify the expression

$f(-3)=9-30=-21$

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

$f(i) = i^2 + 7i - 9$

Step2: Use $i^2=-1$

$f(i) = -1 + 7i - 9$

Step3: Combine constant terms

$f(i)=-10 + 7i$

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

$f(-3+i) = (-3+i)^2 + 7(-3+i) - 9$

Step2: Expand $(-3+i)^2$

$(-3+i)^2=(-3)^2 + 2(-3)(i) + i^2=9-6i-1=8-6i$

Step3: Expand $7(-3+i)$

$7(-3+i)=-21+7i$

Step4: Combine all terms

$f(-3+i)=(8-6i)+(-21+7i)-9$

Step5: Simplify real and imaginary parts

Real parts: $8-21-9=-22$; Imaginary parts: $-6i+7i=i$
$f(-3+i)=-22+i$

Answer:

a. $-21$
b. $-10 + 7i$
c. $-22 + i$