Question

Evaluate the function f(x) = 1/(x-4) when f(1/x)

Answer 1

@phi

Answer 2

substitute the 1/x in place of x inside equation - try it and see what will get ?

Answer 3

f(1/x) = ?

Answer 4

so we will have
\(\large \frac{1}{\frac{1}{x} -4}\)

Answer 5

yes and continue it

Answer 6

i don't know how to evaluate it

Answer 7

first 1/x -4 = ?

Answer 8

\[\frac{ 1 }{ x } - 4\]

i don't know what I am supposed to do. please help me in step-by-step

Answer 9

how you assum a fraction with an integer ?

Answer 10

common denominator ?

Answer 11

1 4
--- - ----- = ?
x 1

Answer 12

the common denominator would be x?

Answer 13

yes

Answer 14

Your "when f(1/x)" is unclear. What are you trying to say here?

You do not yet have an x-value to substitute into the first expression.

Please ensure you've copied down all parts of this problem. Thx.

Answer 15

1/x - 4x/x = (1 - 4x)/x

Answer 16

@mathmale the input value is (1/x)

Answer 17

OK. Leave out the "f" in the second expression.

You could write, "Evaluate the function f(x) = 1/(x-4) when the input to f(x) is 1/x."

Answer 18

@calculusxy yes is right but not forget that there is 1/---

Answer 19

In that case you'd want to evaluate f(1/x); the word "when" should not be there.

Answer 20

@jhonyy9 so what do i do with that numerator?

Answer 21

check what you have got for denominator than rewrite it like how have got firstly using 1/ --- and hope you know that

1 d
------ = 1*----- = ?
a+b a+b
-----
d

hope this is understandably

Answer 22

Evaluate the function f(x) = 1/(x-4) ....

Eliminate the "x" from this expression, replacing it with ( ):

f( ) = 1 / ( ( ) -4).

Finally, write the input "1/x" inside the ( ) and simplify.
This is the same as jhonny9 suggested 'way back:

"jhonyy9
substitute the 1/x in place of x inside equation - try it and see what will get ?"

Answer 23

"Evaluate the function f(x) = 1/(x-4) when f(1/x)" would be clear if re-written as

Evaluate f(1/x) when the function f(x) is defined as f(x) = 1/(x-4)."

Answer 24

@jhonyy9 i have the expression \(\large \frac{1}{\frac{1 - 4x}{x} - 4}\). is the denomintor correct?

Answer 25

wait. get rid of the -4

Answer 26

no - without -4 because you have added to 1/x -4 and have got

Answer 27

\(\large \frac{1 - 4x}{x}\)

Answer 28

yes so

Answer 29

yes and continue it

Answer 30

fyi, once you wrote
\[ \large \frac{1}{\frac{1}{x} -4} \]
that is the answer. Anything after that is changing its form to make it easier to use (or to match it up with an answer choice)

Answer 31

@phi I actually got \(\large \frac{1}{\frac{1 - 4x}{x}}\)

Answer 32

do i have to do anything with the complex fraction?

Answer 33

so and you can simplifie it again

Answer 34

okay so it would be \[\frac{ 1 }{ 1 } \times \frac{x}{1- 4x} = \frac{x}{1-4x}\]

Answer 35

generally people don't like fractions inside fractions, so I would multiply top and bottom by x to clear the denominator.

Answer 36

yes @calculusxy so is right sure

Answer 37

so my answer is \(\large \frac{x}{1 - 4x}\)

Answer 38

yes - right

Answer 39

thanks!

Answer 40

np

was my pleasure

good luck

bye