Evaluate the function at the given values of the independent variable and simplify.
f(x)=
{x^2)-3 if x is less than or equal to -2
{6x+1 if x > -2
a. f(-3)
b. f(0)
c. f(-2)
How do I solve this/what are the correct answers so I can check my work?
I think....
A) -12
B) 1
C)-7
There should be two answers for each because there are two equations.
No, there is one answer for each, since the choice of x determines which equation to use
f(x) = x^2 - 3 , for x ≤ -2
f(x) = 6x+1 , for x > -2
f(-3) = 9 - 3 = 6
f(0) = 6(0) + 1 = 1 , fits 2nd equation
f(-2) = 4-3 = 1 , fits 1st equation.
To evaluate the function at a specific value of the independent variable, you need to substitute the given value into the function expression. Let's solve each part of the problem step by step:
a. f(-3):
Since -3 is less than or equal to -2, we'll use the first part of the function expression: f(x) = (x^2) - 3
Substitute x = -3 into the equation:
f(-3) = (-3)^2 - 3
f(-3) = 9 - 3
f(-3) = 6
b. f(0):
Since 0 is greater than -2, we'll use the second part of the function expression: f(x) = 6x + 1
Substitute x = 0 into the equation:
f(0) = 6(0) + 1
f(0) = 1
c. f(-2):
Since -2 is equal to -2, both parts of the function expression are applicable. However, when this occurs, we use the second part because the problem specifies "if x > -2."
Substitute x = -2 into the equation:
f(-2) = 6(-2) + 1
f(-2) = -12 + 1
f(-2) = -11
Therefore, the answers are:
a. f(-3) = 6
b. f(0) = 1
c. f(-2) = -11