Math Homework Help Please

[MathStudent17314]

I am not sure how to set up/complete this problem. Can someone please explain to me? I'm sure it is simple math but for some reason I cannot understand. Thank you.

Let f(x) = 5x^2 − 3 and g(x) = 5x + 5.
Find the value.
(f ∘ g)(−2)

(f ∘ g)(−2) =

 

[HallsofIvy]

Whoever gave you this problem clearly expects you to know
that \(\displaystyle f\circ g(x)\) means f(g(x)) and \(\displaystyle g\circ f(x)\) means g(f(x)).

What is g(-2)? What is f of that number?

What is f(-2)? What is g of that number?

 

[MathStudent17314]

Whoever gave you this problem clearly expects you to know
that \(\displaystyle f\circ g(x)\) means f(g(x)) and \(\displaystyle g\circ f(x)\) means g(f(x)).

What is g(-2)? What is f of that number?

What is f(-2)? What is g of that number?

My teacher does not explain things very well to me so if I'm being honest I have no idea how to set up an f(g(x)) or g(f(x)) problem.

 

[skeeter]

start easy ... can you find g(-2) ?

 

[MathStudent17314]

start easy ... can you find g(-2) ?

I don't even know how to find g(-2)

 

[skeeter]

I don't even know how to find g(-2)

g(x) = 5x + 5

g(-2) = 5(-2) + 5 = ?

 

[MathStudent17314]

g(x) = 5x + 5

g(-2) = 5(-2) + 5 = ?

Oh I see you just plug in -2 where x is, so it would be -5?

 

[skeeter]

Oh I see you just plug in -2 where x is, so it would be -5?

correct, [MATH]g(-2) = -5[/MATH]
you are given [MATH]f(x) = 5x^2-3[/MATH]
so, [MATH]f[g(-2)] = f(-5) = \, ?[/MATH]

 

[MathStudent17314]

g(-2) = -5
f(-2) = 17
So how would I combine them?

 

[skeeter]

g(-2) = -5
f(-2) = 17
So how would I combine them?

you don't need f(-2) ... you need to find f(-5), because g(-2) = -5

 

[MathStudent17314]

you don't need f(-2) ... you need to find f(-5), because g(-2) = -5

Oh okay so f(-5) = 122

 

[skeeter]

correct ...

[MATH]f[g(-2)] = f(-5) = 5(-5)^2 - 3 = 125 = 3 = 122[/MATH]
you evaluated a composition of functions, one function's output put into another function

 

[MathStudent17314]

correct ...

[MATH]f[g(-2)] = f(-5) = 5(-5)^2 - 3 = 125 = 3 = 122[/MATH]
you evaluated a composition of functions, one function's output put into another function

Thank you so much for explaining it to me I was overthinking it. I will use your help to hopefully complete the rest of the problems.

 

[HallsofIvy]

I don't even know how to find g(-2)

Are you sure you have been going to class? Perhaps you are going to the wrong class?

 

[Steven G]

Unfortunately many students these days do not have a class to go to.

It amazes me that teachers who received their degrees in education are doing such a poor job teaching online. But that is a topic for another thread.