Question

For the following exercises, evaluate the function at the indicated values:

Answer 1

Answer:

The evaluated function for the indicated values is given below.

The value of f(-3) is 20 .

The value of f(2) is 10 .

The value of f(-a) is $2|-3 a-1|$.

The value of -f(a) is $-2|3 a-1|$.

The value of f(a+h) is $2|3 a+3 h-1|$.

Step-by-step explanation:

A function $f(x)=2|3 x-1|$ is given.

It is required to evaluate the function at $f(-3) ; f(2) ; f(-a) ;-f(a) ; f(a+h)$.

To evaluate the function, substitute the indicated values in the given function to determine the output values and simplify the expression.

Step 1 of 5

The given function is $f(x)=2|3 x-1|$.

To evaluate the function at f(-3), substitute -3 in the given function $f(x)=2|3 x-1| \\ f(-3)=2|3(-3)-1| \\ f(-3)=2|-9-1| \\ f(-3)=2|-10| \\ f(-3)=2(10) \\ f(-3)=20$

Step 2 of 5

To evaluate the function at $f(2)$, substitute 2 in the given function.

$f(x)=2|3 x-1| \\ f(2)=2|3(2)-1| \\ f(2)=2|6-1| \\ f(2)=2(5) \\ f(2)=10$

Step 3 of 5

To evaluate the function at f(-a), substitute -a in the given function.

$\begin{aligned}&f(x)=2|3 x-1| \\&f(-a)=2|3(-a)-1| \\&f(-a)=2|-3 a-1|\end{aligned}$

Step 4 of 5

To evaluate the function at -f(a), substitute a in the given function.

$f(x)=2|3 x-1| \\ -f(a)=-2|3(a)-1| \\ -f(a)=-2|3 a-1|$

Step 5 of 5

To evaluate the function at f(a+h), substitute a+h in the given function. $f(x)=2|3 x-1|$

$\begin{aligned}&f(a+h)=2|3(a+h)-1| \\&f(a+h)=2|3 a+3 h-1|\end{aligned}$