f(g(h(x))) – Composite Function with 3 Functions | Algebra Short

Ajouté : 2026-06-05

[00:00:00]Hello, we want to find the formula of the composite function f of g of h of x.

[00:00:08]f of g of h of x.

[00:00:11]So, there are three functions being embedded together here. Now, let's start with the innermost function.

[00:00:18]We want to start with what? g of h of x.

[00:00:22]That is we put h of x inside g.

[00:00:25]So, g is the base. We have two Now, where we see x, we write h of x, which is what? 4 x + 5 then minus three. That is it. So, we have put h of x inside g of x. So, by the time we expand, we have 8 x + 10 then um minus three. That will give us what?

[00:00:51]8 x + seven.

[00:00:54]So, the result of that is 8 x + 7. Now, for the last we have we have we have dealt with this now. Now, put g of h of x inside f. So, f is now the base.

[00:01:04]f is now the base. Therefore, You know, we have gotten g of h of x to be what? 8 x + 7. Now, we now put it inside f. Our f is what? x squared + 1.

[00:01:19]So, now x will now be replaced by 8 x + 7.

[00:01:25]Yes, squared plus one. So, if we expand this by, you know, simple expansion, this one [clears throat] will give you a 64 x squared uh 56 times uh that's plus uh 112 112 x plus 49 then plus one. Yes. That's expansion of this will give you this.

[00:01:48]Then remaining plus one, you write it there. So, that was 64 x squared plus 112 112 x plus 50. So, that's the answer. Bye.