Look at the image please. I need help studying. Thank you kindly. The function m(x) is defined as m(x) = 7√x²-9. Determine three functions,a(x), t(x) and h(x) so m(x) = (ath)(x) and none of the functions are equivalentto y = x. Use the value of x = 6 to show applying the composite functions in orderand using the original composite function produce the same value. Usesimplified exact values in the calculation.

The given function is,The given composite function is,Switch both sides.Substitute the given…

Answered: The function m(x) is defined as m(x) =…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Look at the image please. I need help studying. Thank you kindly.

The function m(x) is defined as m(x) = 7√x²-9. Determine three functions,
a(x), t(x) and h(x) so m(x) = (ath)(x) and none of the functions are equivalent
to y = x. Use the value of x = 6 to show applying the composite functions in order
and using the original composite function produce the same value. Use
simplified exact values in the calculation.

Expert Solution

Step 1: composite function

The given function is,

$m open parentheses x close parentheses equals 7 square root of x squared minus 9 end root$

The given composite function is,

$m open parentheses x close parentheses equals open parentheses a ring operator t ring operator h close parentheses open parentheses x close parentheses$

$m open parentheses x close parentheses equals a open parentheses t open parentheses h open parentheses x close parentheses close parentheses close parentheses$

Switch both sides.

$a open parentheses t open parentheses h open parentheses x close parentheses close parentheses close parentheses equals m open parentheses x close parentheses$

Substitute the given function.

$a open parentheses t open parentheses h open parentheses x close parentheses close parentheses close parentheses equals 7 square root of x squared minus 9 end root$

Now take $h left parenthesis x right parenthesis equals x squared$

$a open parentheses t open parentheses h open parentheses x close parentheses close parentheses close parentheses equals 7 square root of h open parentheses x close parentheses minus 9 end root$

Replace h(x) with x

$a open parentheses t open parentheses x close parentheses close parentheses equals 7 square root of x minus 9 end root$

Now take $t left parenthesis x right parenthesis equals square root of x minus 9 end root$

$a open parentheses t open parentheses x close parentheses close parentheses equals 7 t open parentheses x close parentheses$

Replace t(x) with x

$a open parentheses x close parentheses equals 7 x$

So three functions are:

$h open parentheses x close parentheses equals x squared comma thin space thin space thin space thin space thin space thin space t open parentheses x close parentheses equals square root of x minus 9 end root comma thin space thin space thin space thin space thin space thin space a open parentheses x close parentheses equals 7 x$