Question

I really need help please I can't get this and it is due soon.

Perform the indicated operation.

Answer 1

Az are you gonna help or can i?

Answer 2

(g o f)(x) means you plug in f(x) into g(x)

(g o f)(x) = g(f(x))

let me show you an example

let's say we have
f(x) = x + 1
g(x) = 2x

if we're trying to find (g o f)(x)
that means we take whatever f(x) is equal to
(which is x+1 in this example)

and we plug it into g(x)

pay attention to the colors

\( (g ~o~ f)(x) = g(\color{red}{f(x)})\)

\( f(x) = \color{red}{x+1}\)
\(g(x) = 2x\)

\( g(\color{red}{f(x)}) = g(x+1)\)

and we know that \(g(\color{green}{x}) = 2\color{green}{x}\)

and we see that we have x+1 inside the parenthesis so we get

\( g\color{green}{(x+1)} = 2\color{green}{(x+1})\)

and simplifying that
\( g(x+1) = 2x + 2\)

so your final answer for this example would be

(g o f)(x) = g(f(x)) = 2x + 2

Answer 3

Remember, that was just an example but it's the same concept for your question

(g o f)(x) = g(f(x))

what is f(x) equal to?

and then replace that with 'x' in the g(x) equation and simplify

Answer 4

This is kind of how my teacher explained it I honestly just am not getting it sorry

Answer 5

I am trying to but I cant get it

Answer 6

let's look at your question

g(x) = x^2 + 5
f(x) = 4x - 3

what is f(x) = ???
hint: it's given to you in your question, you just need to restate it

Answer 7

4x-3?

Answer 8

hint:
(a-b)^2 = a^2 - 2ab + b^2