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What can be said about fof^-1(x) of the function: y = x/4 + 3.

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lillyan | Student, Undergraduate | (Level 2) Honors

Posted May 10, 2011 at 4:43 AM via web

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What can be said about fof^-1(x) of the function:

 y = x/4 + 3.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted May 10, 2011 at 10:58 AM (Answer #2)

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We'll write the given function:

y = x/4 + 3

We'll multiply by 4 both sides:

4y = x + 12

We'll use the symmetric property:

x + 12 = 4y

We'll isolate x to the left side. For this reason, we'll subtract 12 both sides:

x = 4y - 12

The inverse function is:

f^-1(x) = 4x - 12

Now, we'll compose the functions:

(fof^-1)(x) = f(f^-1(x))

We'll substitute x by the f^-1(x) in the expression of f(x):

f(f^-1(x)) = f^-1(x)/4 + 3

We'll substitute f^-1(x) by it's expression:

f(f^-1(x)) = (4x - 12)/4 + 3

f(f^-1(x)) = 4x/4 - 12/4 + 3

f(f^-1(x)) = x - 3 + 3

We'll eliminate like terms and we'll get:

f(f^-1(x)) = x

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 11, 2011 at 6:14 AM (Answer #3)

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fof^-1(x)

= f(f^-1(x))

= x, by definition

Here y = x/4 + 3

The inverse function is found by expressing y in terms of x, x = (y - 3)*4. Now interchange y and x. f^-(x) = (x - 3)*4

fof^-1(x)

= f((x - 3)*4)

= (x - 3)*4/4 + 3

= x

This proves that for f(x) = x/4 + 3, fof^-1(x) = x

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