Question

Given the parent functions f(x) = log10 x and g(x) = 5x − 2, what is f(x) • g(x)?

Answer 1

@Astrophysics

Answer 2

\[f(x)g(x) = \log_{10}x (5x-2)\]

Answer 3

You're just multiplying the functions

Answer 4

Thanks! Can I ask one more?

Answer 5

If f(x) = log2 (x + 4), what is f−1(3)?

Answer 6

The \[f^{-1}\] represents inverse

Answer 7

yes:)

Answer 8

To find the inverse:

Replace f(x) with y
Switch x's and y's, so put x where y is and x where y is.
Solve for y
Replace y with f^-1(x)

Answer 9

Once you find the inverse just plug in 3 into the function and evaluate :-)

Answer 10

y=log2(x+4)

Answer 11

good keep going

Answer 12

x=log2(y+4)

Answer 13

right

Answer 14

im confused on how to solve for "Y"

Answer 15

Since it's \[\log_2\] as the base we will have to take the power of 2 to on both sides so the following \[\huge 2^x = 2^{\log_2(y+4)} \implies 2^x = y+4\]

Answer 16

hmm then wouldnt we have to get y alone?

Answer 17

Would the answer be 8?

Answer 18

f(a) =b , hence \(f^{-1} (b) =a\) ok?

Answer 19

we need find \(f^{-1} (3) \) of \(f(x) = log 2(x+4)\), right?
That is just let log 2(x+4) =3, and solve for x.

Answer 20

You can do either way you should get same result

Answer 21

2?

Answer 22

No, \[y=2^x-4 \implies f^{-1}(x) = 2^x-4 \implies f^{-1}(3) = 2^3-4\]

Answer 23

oh! okay so then I got, 4

Answer 24

confirm: \(log (2(x+4))\) or (x+4)*log 2??

Answer 25

Yes, 4 sounds betters :)

Answer 26

2x2x2=4x2=8
8-4=4
:)

Answer 27

I think the original question was \[\log_2(x+4)\] right?

Answer 28

yes

Answer 29

Ok we're good then

Answer 30

Thanks @Loser66

Answer 31

yay! Thanks guysss:)

Answer 32

ok, clear.