Question

Given f(x)=x^2+7 and g(x)=x-4/x. Find (g o f)(-1).
Hint: (g o f)(-1)=g(f(-1))

Answer 1

so have you tried finding f(-1)
and then finding g(put result of f(-1) here)

Answer 2

f(-1) tells us to use f(x)=x^2+7
we know to use f(x)=x^2+7 because of the f in f(-1)

Answer 3

f(x)=x^2+7
we can see here the input is the thing in f( )
example:
f(a)=a^2+7
f(a+1)=(a+1)^2+7
f(input)=(input)^2+7
another example;
f(2)=2^2+7
can you find f(-1)=?

Answer 4

I'm a little lost, sorry.

Answer 5

ok do you see that f(x)=x^2+7
and you are also to find f(-1)?

Answer 6

f(x)=x^2+7
since we want to find f(-1)
we need to replace those x's with -1

Answer 7

Yes.

Answer 8

so can you find f(-1)?

Answer 9

let me know when you have found f(-1)

Answer 10

Would it be f(-1)-1^2+7?

Answer 11

well there should be an equal sign somewhere there

Answer 12

can you simplify (-1)^2+7?

Answer 13

8?

Answer 14

yes
f(-1)=(-1)^2+7=(-1)(-1)+7=1+7=8
so f(-1)=8
so f(-1) is 8
now we had to find g(f(-1))
we just found that inside thing the f(-1) thing to be 8
replace f(-1) with 8
you are now really wanting to find g(8)

Answer 15

g(8) tells us to use the expression named g

Answer 16

g looks likes
g(x)=x-4/x

Answer 17

just replace the old input x with the new input 8

Answer 18

simplify and then you are done

Answer 19

So, g(8)=x-4/x?

Answer 20

you have to replace all the x's with 8
not just one of the x's

Answer 21

whatever you replace the first x with you have to replace the other x's on the other side also

Answer 22

g(8)=8-4/8?

Answer 23

yes

Answer 24

So simplify 8-4/8?

Answer 25

@freckles

Answer 26

yes

Answer 27

I don't think teachers like unsimplified answers :p

Answer 28

7.5 is my answer?

Answer 29

And no, they don't lol.

Answer 30

Thank you so much for the help!

Answer 31

for me to check your answer
I have to know one this
is it \[g(x)=\frac{x-4}{x} \text{ or } g(x)=x-\frac{4}{x}\]

Answer 32

First one.

Answer 33

so it is actually
g(x)=(x-4)/x not g(x)=x-4/x

so g(8)=(8-4)/8=4/8=1/2 or .5

Answer 34

\[f(x)=x^2+7 \\ g(x)=\frac{x-4}{x} \\ g(f(-1)) = g((-1)^2+7)=g(1+7)=g(8)=\frac{8-4}{8}=\frac{4}{8}=\frac{1}{2}\]

Answer 35

So what would be the answer?

Answer 36

well we just got that g(f(-1))=1/2
and we were looking for the value of g(f(-1))
so we are done