For the given functions f and g, find the requested...

For the given functions f and g, find the requested composite function value. 3) f(x) = (x - 6) / x, g(x) = x^2 + 9; Find (g ? f)(-2). A) 25 B) 145/16 C) 13 D) 7/13 Evaluate the expression using the values given in the table. 4) (g ? f)(1) x | 1 | 5 | 10 | 12 f(x) | -2 | 10 | 3 | 15 x | -5 | -2 | 1 | 3 g(x) | 1 | -8 | 5 | 10 A) 5 B) 10 C) -2 D) -8

Transcript

00:01 Okay, in this problem, we have to find f of g of x, where f of x, f of x equals x minus six over x.

00:11 And then g of x equals, where is it, x squared plus nine? x squared plus nine.

00:19 All right, and we need to find f of g of x, right? so that f of g of x, i'm going to write that instead as f of g of x.

00:29 That's how i help.

00:30 It helps me to really know what i'm doing.

00:32 So i'm going to take g of x and plug it in to f of x.

00:36 So that means i'm going to have, actually, i'm going to simplify this x, this f of x into 1 minus 6 over x.

00:45 That's going to be a lot easier, i think, to substitute x squared plus 9.

00:49 All right.

00:49 So i'm going to have 1 minus 6 over x squared plus 9.

00:52 This is going to equal 1 minus 6 over x squared plus, where is it? plus nine plus nine that kind of looks like an and right so plus nine right now i just need to find that for negative two so this is f of g of x so i'm going to plug in f of g of two right and now negative two excuse me i've read misread that negative two that just means i'm going to plug in negative two for x right here and i'm going to get equal to one minus six over negative two parentheses squared plus nine.

01:29 All right.

01:30 Now we have that two squared is going to be, or negative two squared, it's going to be four, four plus nine is 13.

01:35 So this is equal to one minus six over 13.

01:41 And six over 13.

01:42 So that's going to be 13th minus.

01:44 So what is 13 minus six? that's going to be seven...

Question

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