Domain kodomain dan range suatu fungsi

Assalamualaikum warahmatullahi wabarakatuh. Meet again with our channel, Matematika Hebat. In this video, we will try to discuss the domain and rank of a function.

But before we continue, don't forget to like, subscribe, comment, and share our video. Hopefully the video is useful and easy to use, it can be a practice for us later. Now let's just discuss the example of the question. Pay attention to the first question, given the function f = 4x + 2, determine the domain, codomain, and rank.

Even though the steps or the way to solve it is actually very easy. Pay attention. It should be remembered that if the function given is not a form of division and not a form of root, then for the domain, we just write x where? x element of the real number.

Whereas for the codomain, because there is no limit here, then for the codomain, we just write x where? x real element. Remember, usually it's written x 0, 4. This is the limit. Then the codomain will be different. Whereas for our question this time, there is no limit. So we just write it like this.

Meanwhile, for rank, first we have to find the inverse of this fx function. Notice how, we define this fx function as y. y = 4x + 2 Now our task is how to make the shape of x = 4x + 2 = y.

4x = y, then positive 2, then right, so negative 2. Then x = y - 2/4. Then the inverse function of the fx function is f inverse x = x - 2/4. Now, pay attention to the inverse function again.

Because the inverse result, the X parabola is not placed at the bottom, and it is also not a root, then for the result area or the range, which is Y, where Y is the real number element. Remember again, if the inverse result is not a fraction, the meaning of the fraction here, the X parabola is not placed at the bottom.

And it's not a root, so for the rank, it's like this, Y where Y is the real number. This is the answer for the first question. Now we go to the second question. Given the function f = x, the code is -6x + 7, determine the domain, codomain, and the rank. Okay. Remember once again, for the domain,

make sure the function given is not a fraction, nor a root. So for the domain, we just write it, which is x, where? x, element, real number. Then for the domain code, because here it doesn't have a limit, then for the domain code, we also write it, x, where? x, element, real number. Meanwhile for the rank, or the result area,

we have to find the inverse of this function first. Remember the way, where we use f of x as y. y = x^2 - 6x + 7. This is the shape of y. Now, our task is how to make the shape of x. Now, pay attention to the way. y =

The shape of x^2 - 6x + 7, we change the way of writing it. x is reduced, pay attention here. The number in the middle here, okay, here it is not written as reduced or added. The number in the middle here is -6 divided by 2. We get the result -3, close the comma, square it. Okay, then it is reduced by the number here, we got it earlier.

3, then squared, then plus 7. The number behind here. Next, y = -3^2 -3^2 = 9, then plus 7. y = -9 + 7 = -2

Continue, y then negative 2 move to the left, so positive 2, equal to in the curve, x minus 3, decoded. Remember, to remove this coded sign, of course, the number on the left and right, we multiply it by the form of root, or we multiply it by the middle bracket. So here it becomes, root of y plus 2, equal to

x - 3. Continue again. To make it easier, we change the position. x - 3 = √ . Then x = √ . Then,

The inverse of this fx function is f inverse x equals the root of y times x. x plus 2 plus 3. This is the inverse form. Meanwhile, for the rank, pay attention, because it is a root here, then the requirement is that the number in the root must be greater than 0. I mean the same size. Not just big, but the same size.

Then here, pay attention, x is only the small one in the root. Add 2, equal to 0. Then x equal to positive 2, move to the right, so negative 2. Then for the range, which is y, okay sorry, y, where y must be equal to negative 2.

and Y is the element of the del-number. This is the answer for question number 2. Next, now pay attention to question number 3. The root. Given the function f = root of 2x-4. Determine the domain, codomain, and the range. Pay attention here. For the domain, it's different. Well, for the domain, because the function f is the root,

Remember, the root is the condition that it is defined, there is a result, the integer must be equal to 0. So here for the domain we look for first, take the integer, 2x - 4, the condition must be equal to 0. 2x = -4, move to the right, so it's positive 4, so x = 4 divided by 2.

Next, we calculate X = 4/2, the hc is 2. Then for the domain or the original area, which is X, where X must be equal to 2 and X is the real number element. This is for the domain.

Continue again, for the codomain, because here it has no limit, then we write the codomain directly, where? x, element, real number. Meanwhile, for the rank, for the rank whose function is fx in the form of root,

we just write it directly, Y, where Y must be equal to 0, and Y is the real number element. Remember again, for the effect function that is given if it is root, then for the range area, we don't need to look for the inverse. Why? Remember again, a function, okay, if it is root, then it will be defined

or have the result if the inside is greater than 0. Or in other words, the fx function that is root will not always be negative. If it is root, then here, y must be greater than 0. Okay, this is how to determine the domain to domain range whose fx function is root. Finally, now we enter the form of division again.

Given the function f = 2x-6/4-2x, determine the domain, codomain, and the ring. Okay, for the domain first. Because it is a fraction, then make sure the number below is not equal to 0. Okay, then here we write 4-2x, it can't be equal to 0.

Then negative 2x cannot be equal to positive 4, so it will be negative 4. Then x cannot be equal to negative 4 divided by negative 2. Then x cannot be equal to negative 4 divided by negative 2, so it will be positive 2. Then for the domain here, x cannot be equal to 2. And x is the real number element.

Then for the domain, remember once again, if it doesn't have a limit, the function given doesn't have a limit, then for the domain, we just write x where? x element of the real number. And for the rank or the result area, of course we have to find the inverse of the fx function first. How? Pay attention. We can use the fx function as y.

y = 2x - 6 per 4 - 2x. This is the shape of y =. Our task now is how to make the shape of x =. The way is, pay attention here, we multiply first. y * 4 = 4y. Then y * -2x = -2xy. = 2x - 6.

Every time there is an x, we move it to the left. If there is no x, we move it to the right. So, it becomes negative 2xy, then 2x moves to the left, which is negative 2x. Same with positive 4y, moves to the right, which is negative 4y, then it is reduced to 6.

Next, x is pulled out, then the remaining is -2y -2 = -4y -6 Then x is the same as -4y -6 times -2y -2 Next, pay attention here, then x is the same as, pay attention because the top and bottom here are negative, all the numbers here we multiply by a negative sign

So what happens? Of course it becomes +4y +6, plus 2y +2. Then, pay attention here, we continue above here.

The inverse form of the function f = f inverse x = 4x + 6/2x + 2. This is the inverse form. Because the inverse form is a square, then the result area or rank, the number below it cannot be equal to 0.

So here we write, 2x + 2, it can't be equal to 0. 2x can't be equal to positive 2, move to the right, it becomes negative 2. So x can't be equal to negative 2, divide by 2, the characteristic is negative 1.

The answer is Y, where Y is not equal to negative 1, and Y is the element of the real number. And this is the answer. That's all for our short tutorial. Hopefully the video is useful. If not, we apologize. We close with Assalamualaikum Warahmatullahi Wabarakatuh.