1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lord [1]
3 years ago
13

Can someone please help me with this last one. I am totally lost and don’t understand

Mathematics
1 answer:
Ad libitum [116K]3 years ago
4 0

Answer:

g(-4) = -1

g(-1) = -1

g(1) = 3

Explanation:

If you are given a function that is defined by a system of equations associated with certain intervals of x, just find which interval makes x true, and then substitute x into the equation of that interval.

For example, given g(-4), this is an expression which is asking for the value of the equation when x = -4. So -4 is not ≥ 2, so ¼x - 1 will not be used. -4 is also not ≤ -1 and ≤ 2, so -(x - 1)² + 3 will not be used either. So in turn, we will just use -1 which is always -1 so g(-4) will just be -1, right because there is no x variable in -1 so it will always be the same.

Using the same idea as before g(-1) is g(x) when x = -1 so -1 will not be a solution because -1 is not less than -1 (< -1). -1 is not ≥ 2 either so we will be using the second equation because -1 is part of the interval -1≤x≤2 (it is a solution to this inequality), therefore -(x - 1)² + 3 will be used.

As x = -1, -(x - 1)² + 3 = -(-1 - 1)² + 3 = -(-2)² + 3 = -4 + 3 = -1.

It is a coincidence that g(-1) = -1.

Now for g(1), where g(x) has an input of 1 or the value of the function where x = 1, we will not use the first equation because x = 1 → x < -1 → 1 < -1 [this is false because 1 is never less than -1], so we will not use -1.

We will use -(x - 1)² + 3 again because 1 is not ≥ 2, 1≥2 [this is also false]. And -1 ≤ 1 < 2 [This is a true statement]. Therefore g(1) = -(1 - 1)² + 3 = -(0)² + 3 = 3

You might be interested in
the volume of this rectangular prism is 5x^3. what does the coefficient 5 mean in terms of the problem?
Fofino [41]
it's C, assuming x always has the same value
8 0
3 years ago
Read 2 more answers
Please help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
vladimir2022 [97]
First one is 42
second is 24
Third is 12
3 0
2 years ago
Read 2 more answers
A= 1 2 3 4 5 is the solution of a set of the variable equation<br> 3x=15
Harrizon [31]

Answer:

3x = 15

x = 15/3

x  =5

7 0
2 years ago
A right angle and an isosceles triangle is always sometimes or never true
blsea [12.9K]

Answer: sometimes!

Step-by-step explanation: I hope this helps!

6 0
3 years ago
Read 2 more answers
Two sides of a right triangle measure 5 inches and 6 inches, and the third side measures√61 inches.The length of the third side
lesantik [10]
The length of the third side is about 7.81 inches and the perimeter of the triangle is about 18.81 inches
6 0
3 years ago
Read 2 more answers
Other questions:
  • Solve the literal equation cy−7=5d+3ycy−7=5d+3y for yy.
    14·1 answer
  • lynn, jude and anne were given the function f(x)=-2x^2+32, and they were asked to find f(3). lynns answer was 14, judes answer w
    5·1 answer
  • What is a function in math i am stuck on what the slope is and other things like it.
    13·1 answer
  • PLEASE SOMEONE HELP ME OUT I DON'T UNDERSTAND HOW TO DO THIS ! I WILL GIVE BRAINLIEST FOR YOUR ANSWER
    5·2 answers
  • Convert 35 kilometers to miles
    15·2 answers
  • Kharon needs to write 3 book reports with b pages and 3 science reports with s pages during the school year. Write an algebraic
    11·1 answer
  • Create a 10 question survey with quantitative variables (number) on a topic you are interested in. Think of questions where 0 is
    11·1 answer
  • What is 6/10 plus 4/10
    13·2 answers
  • X^5y^4+x^3y^4<br><br>x <br><br>5<br><br> y <br><br>4<br><br> +x <br><br>3<br><br> y <br><br>4
    15·1 answer
  • Find the x-intercept and y-intercept of the line.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!