Question

for the following exercise, evaluate the function ( f ) at the indicated values ( f(3) ), ( f(-2) ), ( f(-a) ), ( -f(a) ), ( f(a + h) ). simplify your results.
( f(x) = 2x + 4 )
( f(3) = )
( f(-2) = )
( f(-a) = )
( -f(a) = )
( f(a + h) = )

Explanation:

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

$f(3)=2(3)+4$

Step2: Calculate $f(3)$

$f(3)=6+4=10$

Step3: Substitute $x=-2$ into $f(x)$

$f(-2)=2(-2)+4$

Step4: Calculate $f(-2)$

$f(-2)=-4+4=0$

Step5: Substitute $x=-a$ into $f(x)$

$f(-a)=2(-a)+4$

Step6: Simplify $f(-a)$

$f(-a)=-2a+4$

Step7: Substitute $x=a$ into $f(x)$, then negate

$-f(a)=-(2a+4)$

Step8: Simplify $-f(a)$

$-f(a)=-2a-4$

Step9: Substitute $x=a+h$ into $f(x)$

$f(a+h)=2(a+h)+4$

Step10: Simplify $f(a+h)$

$f(a+h)=2a+2h+4$

Answer:

$f(3)=10$
$f(-2)=0$
$f(-a)=-2a+4$
$-f(a)=-2a-4$
$f(a+h)=2a+2h+4$