Question

really confused.

Given the function f(x) = 0.5(3)x, what is the value of f−1(7)?

0.565

1.140

1.771

2.402

Answer 1

the -1 is an exponent to the F

like so: \[f^-1 \]

Answer 2

Is that
f(x) = \(0.5*3x\)
Or is it f(x) = \(0.5^3x\) ?

Answer 3

wait, its 0.5 x (3) ^ x

Answer 4

\(f^{-1}(x)\) means that it is an inverse of the function \(f(x)\)

So, When \(f(x) = 0.5 * 3 ^ x\) we can write that as \(y = 0.5 * 3 ^ x\)

Then the inverse of this would be [by switching the x and the y values]

\(x = 0.5 * 3 ^ y\)

So \(\frac{x}{0.5} = 3 ^ y\)

Or \[y =\log_{3} \frac{x}{0.5} \]

Getting this? :)

Answer 5

yeah i understand that.

Answer 6

Now just substitute the value of 7 in place of x and then find

y = log_3 (14)

Got it right? :D

Answer 7

my calculator is telling me that log_3 (14) is 6.679 but that's none of my answers.
im still confused. :(

Answer 8

Try again, my prediction is the answer should be greater than 2 and lesser than 3.

3 ^ 6.679 = 729 ++

Answer 9

Do you see why? :D

To check you can just take random natural numbers and find a suitable range.

For eg. we want

3 ^ (something) = 54

If that something is 2 then 3^3 = 27

And if it is 4 then 3 ^ 4 = 81

Then we can definitively say that that something lies between (3 --> 4)

Getting me? :)

Answer 10

yes

Answer 11

So the answer of this question should be?

Answer 12

2.402 would be the only thing that is in between the range of greater than two lesser than three.

Answer 13

Excellent, you got it! (y)

Answer 14

can you help with one more? similar to this one.

Answer 15

I'd suggest you try it first and if you have any question after that, then ask! :D

Answer 16

this one has to do with a log.

Answer 17

Fine, let me see if i can help. :)

Answer 18

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

0

2

4

8

Answer 19

@AkashdeepDeb

Answer 20

Alright so what was the initial procedure? What did we do in the beginning?

Answer 21

@mallorysipp234 ?

Answer 22

switch the x and the y.

Answer 23

Yes, so what do you get after doing that?

Answer 24

wouldn't it be log_2 (x+4) = 3

Answer 25

f(x) = log2 (x + 4)

y = log2 (x+4)

SWITH THEM NOW. :D

x = log2 (y+4)

So NOW we have to find y when x=3

3 = log2 (y+4) [And thus we can find y]

Now do you know how to convert this function to exponential form [a ^ b = c form]

Answer 26

no :(

Answer 27

Hint:

\(a^b = c \) can be written as \(log_{a}~ c = b\)

try now? :D

Answer 28

Learn that ^ It is very important in Math. :)

Answer 29

so log_2(3) = (y+4) ?????

Answer 30

alright ill write it down in my notes

Answer 31

Not quite.

3 = log2 (y+4)
in a better format is \( log_2 (y+4) = 3\)

So when 2 is the base and 3 is the power. We can say that

\(2^3 = 8 = (y+4)\)

Did you get this? If you didn't, ask, I'll explain it again.

Answer 32

yeah! that makes sense.

Answer 33

so y is 4.

Answer 34

Correct.

Answer 35

alright! (: i get it.. thank you!

Answer 36

:)