Question

HELP I forgot how to solve this!

Answer 1

HI!

Answer 2

for the first one, find \(g(-1)\)
once you get that plug it in for \(f\)

Answer 3

you know how to find \(g(-1)\)?

Answer 4

sadly no :(

Answer 5

\[g(x)=\frac{1}{x}\\
g(\heartsuit)=\frac{1}{\heartsuit}\\
g(-1)=?\]

Answer 6

-1?

Answer 7

yes

Answer 8

next find \(f(-1)\)

Answer 9

-1?

Answer 10

oh no

Answer 11

\[f(x)=x^2+9x\\
f(\spadesuit)=\spadesuit^2+9\spadesuit\\
f(\xi)=\xi^2+9\xi\\
f(-1)=?\]

Answer 12

@misty1212 sorry my computer crashed i got -8

Answer 13

yes; that is the answer

Answer 14

so in the first blank i put -1 and in the second i put -8?

Answer 15

NO

Answer 16

that was the answer to the first one only
\[f(g(-1))=f(-1)=-8\]

Answer 17

oh ok can you help me with the equation for the second part?

Answer 18

g(f(1/2)) means find the value of f(1/2) and then find g of this value.

Answer 19

It's more productive if you understand what g(f(x)) means.
If g(x) = 1/x
then g(f(x)) means replace the x in g(x) = 1/x with f(x), giving us 1/f(x)
So g(f(1/2)) = 1/f(1/2)

Answer 20

do i did that and got 19/4?

Answer 21

f(1/2) = (1/2)^2 +9(1/2) = 1/4 + 9/2 = 19/4
Then g(f(1/2)) = g(19/4)

Answer 22

@mww so the answer for the second part is 19/4?

Answer 23

f(1/2) = 19/4
But what is g(f(1/2)) = g(19/4) ?
You need to refer to your g function to find g(19/4) ; it's a two step question

Answer 24

im so confused can you please work it out with me?

Answer 25

what is g(x)?

Answer 26

19/4

Answer 27

never mind its 1/x

Answer 28

ok so g(x) = 1/x means to find what g is we take the reciprocal of the input, x

Answer 29

which is 19/4?

Answer 30

f(x) tells us we must square the input and add 9 lots of the input (x^2 + 9x)
So f(1/2) = 19/4 by subbing in when our input in 1/2.

However g(f(x)) means we take the reciprocal of f(x) our input
So g(f(1/2)) means we do 1/f(1/2) = 1/(19/4) = 4/19

Answer 31

oh so its 4/19?

Answer 32

do you get how we obtained that answer?

This is called function composition or function of a function.
The answer you get from one function you plug in as the input for the new function as shown below: