Question

given f(x)= x2+3 and g(x)=x+5/x find (gof)(4)

Answer 1

(gof)(x)=g(f(x)). So instead of x's in g(x) you will have f(x). Can you continue from here?

Answer 2

@Traxter i still dont understand, can you work through it with me?

Answer 3

(gof)(x)=g(f(x))=g(x^2+3)=(x^2+3)+5/(x^2+3)
When we evaluate at x=4, we get (gof)(4)=19+5/(19)

Answer 4

(Which simplifies to 366/19)

Answer 5

@Traxter so its like 19.3?

Answer 6

Yes, to one decimal place.

Answer 7

@Traxter it cant be, its either 14/19 or 24/19

Answer 8

When you wrote f(x)=x2+3, did you mean x squared by x2?

Answer 9

@Traxter Yes

Answer 10

@Traxter Sorry, my bad

Answer 11

given f(x)= x^2+3 and g(x)=(x+5)/x find (gof)(4)

Answer 12

Ok so we are taking g(x) composed with f(x) for x=4. So we will be taking g(f(4)).
f(4)=4^2+3=16+3=19. Sub this into g(x).
g(19)=(19+5)/19=24/19.
It was the lack of brackets in g(x) that confused me. Note that x+5/x is not the same as (x+5)/x

Answer 13

\[ f(x)= x^2+3\]
\[g(x)=\frac{x+5}{x}\] like that?

Answer 14

o then keep it x+5

Answer 15

i just wanted to not that x+5 is all over x

Answer 16

Then the last answer I gave is correct. Do you follow the working?

Answer 17

i'm so confused then because the answers dont match up. they have to be either 14/19 24/19 15 or -15

Answer 18

@Traxter

Answer 19

is \(g(x)=\frac{x+5}{x}\) right?

Answer 20

yes

Answer 21

Yes and I told you the answer is 24/19. Look through my solution:

"Ok so we are taking g(x) composed with f(x) for x=4. So we will be taking g(f(4)). f(4)=4^2+3=16+3=19. Sub this into g(x). g(19)=(19+5)/19=24/19. It was the lack of brackets in g(x) that confused me. Note that x+5/x is not the same as (x+5)/x"

Answer 22

@Traxter ah i c

Answer 23

@Traxter has it for sure