The following questions I don't understand, could you please help me? Thanxs!
Evaluate the piecewise function at the given value of the independent variable.
3. g(x){x^2+2 if x can not equal 2 {x+8 if x=2
Determine g(-5)
options: a.-5, b.3, c.3/7, d. -27/7
4.f(x) {-5x+4 if x< -3 {2x+3 if x > or equal to -3
Determine f(-7)
options: a.39, b.-10, c.42, d.35
On the first g(-5)=25+2=27
On the second f(-7)=35+4=39
To evaluate the function g(x) and find g(-5), we substitute -5 into the function and simplify:
g(x) = {x^2 + 2 if x ≠ 2
{x + 8 if x = 2
Since -5 ≠ 2, we use the first part of the function:
g(-5) = (-5)^2 + 2
= 25 + 2
= 27
Therefore, the answer is 27.
Sure, I can help you understand how to evaluate these piecewise functions. Let's start with the first question:
3. To evaluate the piecewise function g(x), we need to consider both cases separately.
- For the first case, where x is not equal to 2, we substitute x = -5 into the expression x^2 + 2.
g(-5) = (-5)^2 + 2 = 25 + 2 = 27.
- For the second case, where x = 2, we substitute x = 2 into the expression x + 8.
g(2) = 2 + 8 = 10.
Since we are asked to determine g(-5), which falls under the first case, the answer is 27. So, the correct option is d. -27/7.
Now, let's move on to the second question:
4. Similar to the previous question, we will evaluate the piecewise function f(x) by considering the two cases separately.
- For the first case, when x < -3, we substitute x = -7 into the expression -5x + 4.
f(-7) = -5(-7) + 4 = 35 + 4 = 39.
Since we are asked to determine f(-7), which falls under the first case, the answer is 39. So, the correct option is a. 39.
I hope this helps you understand how to evaluate piecewise functions. If you have any more questions, feel free to ask!