Question

Really easy, just check my answer.
If f (x) = 4x^2+3 and g (x ) = 1/3x+4 , find ( f of g^-1)(3).

I got 39 @rishavraj

Answer 1

did u calculate the \[g^{-1}(x)\]

Answer 2

Yes, and i got 3x-12 = y

Answer 3

hold on solving :P

Answer 4

did u solve?

Answer 5

lets say g(x)=y

\(g^{-1}(x)=\large\frac{1}{3(y-4)}\)

Answer 6

um ok?

Answer 7

u got options...coz i am getting fractions

Answer 8

ok to find g^-1 you simply find the inverse of g (x)

Answer 9

ok now just plug in \(g^{-1}(x)\) into f(x) in place of x to get (f of g^-1)(x)

Answer 10

so thats 3x-12, then plug in 3, then use that value in f

Answer 11

wait im confused

Answer 12

@Alina123 there???

Answer 13

whts the value of g-1(x) ??

Answer 14

its just the inverse of g(x)

Answer 15

lol i dint mean tht.... u calculated g-1(x) right??/

Answer 16

yeh i got 3x-12

Answer 17

Hello

Answer 18

yeah

Answer 19

um please help me with my question i dont have time

Answer 20

\[g^{-1} (x) = \frac{ 1 - 4x }{ 3x }\]

Answer 21

this doesnt help what will my answer overall be?

Answer 22

no no .... now u need to calculate
\[g^{-1}(3)\]

Answer 23

ok what do u get then

Answer 24

787/81

Answer 25

9.7

Answer 26

keep it in fraction

Answer 27

Inverse the g function, input it into the function of x, with x being 3 as per g(3)

Answer 28

Do you know how to inverse a function?

Answer 29

yes

Answer 30

i get -3 then

Answer 31

Let me try solve it

Answer 32

Inverse of g(x)

\[g (x )^-1 = \frac{ 1 }{ 3 }x +4 \]

\[y = \frac{ 1 }{ 3 }x + 4\]

Switch every x with every y

\[x = \frac{ 1 }{ 3 }y + 4 \]

Solve for y

\[y = 3(x -4)\]

Therefore,

\[g(x)^{-1} = 3(x-4)\]

Answer 33

Does this make sense to you?

Answer 34

yes i get this part

Answer 35

i then substitute 3 and get -3

Answer 36

@Alina123 it was \[g(x) = \frac{ 1 }{ 3 }x + 4\]
not
\[g(x) = \frac{ 1 }{ 3x + 4 }\]
-_-

Answer 37

No, cause @shadowlegendx his way was the way i was going for

Answer 38

I got 39 as well.

Inputting -3 from g(3)^-1