Could you explain to me how to these type of problems? I checked in my book and it is still confusing.
Evalute the piecewise function at the given value of the independent variable.
1. g(x)= {x^2+2 if x cannont equal 2, x+8 if x=2
Determine g(-5).
2. f(x) {-5x+4 if x <-3, 2x+3 if x > or equal to -3
Determine f(-7)
If x is -5, it is not two. g(x)=27
To evaluate a piecewise function at a given value, you need to follow these steps:
1. Identify the condition(s) or range(s) for which the function is defined differently. In each of the example problems you provided, there are two separate pieces or conditions defined for the functions.
2. Based on the given value, determine which condition applies.
3. Apply the corresponding formula or expression for the condition that matches the given value.
Now let's solve the two example problems you provided:
1. g(x) = {x^2 + 2 if x cannot equal 2, x + 8 if x = 2}
Given: g(-5)
Since the given value is -5, the condition "x cannot equal 2" is applicable. Therefore, we will use the expression "x^2 + 2" to evaluate g(-5).
Substituting -5 for x: g(-5) = (-5)^2 + 2
= 25 + 2
= 27
So, g(-5) = 27.
2. f(x) = {-5x + 4 if x < -3, 2x + 3 if x ≥ -3}
Given: f(-7)
Since the given value is -7, the condition "x < -3" is applicable. Thus, we will use the expression "-5x + 4" to evaluate f(-7).
Substituting -7 for x: f(-7) = (-5)(-7) + 4
= 35 + 4
= 39
So, f(-7) = 39.
By applying the specific formula or expression corresponding to the given value, you can evaluate piecewise functions effectively.