Question

find the indicated function composition and evaluate. find (g*f)(2) f(x)=squareroot of (2x+9) g(x)=4x^2

Answer 1

Hey glea :)
Is that a multiplication star?
Or did you mean for it to be the composition symbol? \(\Large\rm (g\circ f)(2)\)

Answer 2

what you typed
dont know how to make one

Answer 3

\[\Large\rm \color{orangered}{f(x)=\sqrt{2x+9}},\qquad\qquad g(x)=4x^2\]

Answer 4

I prefer to use this notation, I think it makes more sense.
\[\Large\rm (g \circ f)(x)=\quad g(f(x))\]Hopefully you've seen it before :o

Answer 5

ya ive seen it both ways

Answer 6

So we're taking our function g,\[\Large\rm g(\color{royalblue}{x})=4(\color{royalblue}{x})^2\]And instead of plugging x into the function, we're plugging f(x) into it,\[\Large\rm g(\color{orangered}{f(x)})=4(\color{orangered}{f(x)})^2\]

Answer 7

\[\Large\rm g(\color{orangered}{f(x)})=4(\color{orangered}{\sqrt{2x+9}})^2\]

Answer 8

And then we're evaluating this composition at x=2,\[\Large\rm g(\color{orangered}{f(2)})=4(\color{orangered}{\sqrt{2\cdot 2+9}})^2\]

Answer 9

What'd you think? :d
Any of that too crazy?

Answer 10

so 52?

Answer 11

Yay good job \c:/

Answer 12

and you do the same by plugging g into f tosee if they come out the same?

Answer 13

Mmmmm no.
Unless you're trying to verify that g(x) and f(x) are inverse functions.
Were we trying to do something like that? :o

Otherwise we're done with the problem.

Answer 14

no didnt know if i had to show f(g(2))

Answer 15

We solved this: \(\Large\rm (g\circ f)(2)\)

That would correspond to a different problem: \(\Large\rm (f\circ g)(2)\)

So nah, we don't need to worry about that :)

Answer 16

k thanks