Suppose that the functions f and g are defined as...

Suppose that the functions f and g are defined as follows. f(x) = 1 / (4x^2 + 3) g(x) = sqrt(5x - 4) Find f - g and f * g. Then, give their domains using interval notation. (f - g)(x) = [ ] Domain of f - g : [ ] (f * g)(x) = [ ] Domain of f * g : [ ]

Transcript

00:01 Alright, on this one we have two functions f of x and g of x.

00:04 So our f of x is equal to negative 2x plus 3, excuse me, and then our g of x is equal to the square root of 5x minus 1.

00:15 Alright, so first we have to do f plus g.

00:17 So f plus g of x is going to be equal to, well that's going to be really easy, it's just going to be equal to negative 2x plus 3 plus the square root of 5x minus 1.

00:30 Alright, and that's all we can do.

00:32 There's zero else that we can do.

00:34 These are no like terms.

00:36 So the domain of that is going to be everything that where our square root has to be positive, or at least non -negative.

00:46 So that has to be, 5x minus 1 has to be greater than or equal to 0.

00:52 So 5x minus 1 has to be greater than or equal to 0.

00:55 So that means that 5x has to be greater than or equal to 1.

00:58 So that means that x has to be greater than or equal to 1 fifth.

01:01 So that's going to be our domain.

01:03 It's going to be the union of these two intervals.

01:08 And that's going to be, i'm going to actually, i'm going to actually just get that out of the way because i fear that i'm going to run out of room with my whiteboard.

01:17 So i'm going to say that our interval is going to be everything from negative infinity up to 1 fifth.

01:22 It can't include 1 fifth, we're going to union that.

01:25 Well actually it just has to be greater than, i'm sorry, it has to be greater than or equal to 1 fifth.

01:30 So that's going to be just one thing.

01:33 It's going to be 1 fifth up to positive infinity.

01:36 So that's going to be our domain for f plus g of x.

01:40 Now let's move on to the harder one...

Question

Suppose that the functions f and g are defined as follows. f(x) = 1 / (4x^2 + 3) g(x) = sqrt(5x - 4) Find f - g and f * g. Then, give their domains using interval notation. (f - g)(x) = [ ] Domain of f - g : [ ] (f * g)(x) = [ ] Domain of f * g : [ ]

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