Angelica is working on function machines. She has two machines g(x)=square root x-5 and h(x)= x^2-6. she wants to put them in order so that the output of the first machine becomes the input of the second. she wants to use a beginning input of 6.a) in what order must she put the machines to get a final output of 5.
b)is it possible for her to get a final output of -5? if so,show how she could do that. If not explain why not.

PLEASE HELP!

Answers

Answer 1

Answer: $g(h(x))=√(x^2-6-5)=√(x^2-11)\ng(h(6))=√(6^2-11)=√(36-11)=√(25)=5$

a)
$h(x)$ is the input for $g(x)$ , so $h(x)$ must be first

b)
It's impossible for $g(h(x)=√(x^2-11)$ , because its value is always non-negative for any x. Let's see what about $h(g(x))$ .

$h(g(x))=(√(x-5))^2-6=x-5-6=x-11$

The result is a non-constant linear function, so its value can be any real number, including -5. You can calculate for what x it's equal to -5.

$x-11=-5\nx=6$

$x-11=-5\nx=6$

Answer 2

Answer:

a) To get a final output of 5 , she must first input 6 into machine h(x) , then the result from machine h(x) is input back to machine g(x).

b) It is possible to get a final output of -5. It could be done by first input 6 into machine g(x) , then the result from machine g(x) is input back to machine h(x).

Further explanation

Function is a relation which each member of the domain is mapped onto exactly one member of the codomain.

There are many types of functions in mathematics such as :

Linear Function → f(x) = ax + b

Quadratic Function → f(x) = ax² + bx + c
Trigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan x
Logarithmic function → f(x) = ln x
Polynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...

If function f : x → y , then inverse function f⁻¹ : y → x

Let us now tackle the problem!

This problem is about Composition of Functions.

Question a:

Given:

$g(x) = √(x - 5)$

$h(x) = x^2 - 6$

$( h \circ g )( x ) = h ( g ( x ) )$

$( h \circ g )( x ) = h ( \sqrt {x - 5} )$

$( h \circ g )( x ) = (\sqrt {x - 5})^2 - 6$

$( h \circ g )( x ) = x - 5 - 6$

$( h \circ g )( x ) = x - 11$

$( h \circ g )( 6 ) = 6 - 11$

$\large {\boxed {( h \circ g )( 6 ) = -5 } }$

$( g \circ h )( x ) = g ( h ( x ) )$

$( g \circ h )( x ) = g ( x^2 - 6 )$

$( g \circ h )( x ) = \sqrt {( x^2 - 6 ) - 5 }$

$( g \circ h )( x ) = \sqrt { x^2 - 11 }$

$( g \circ h )( 6 ) = \sqrt { 6^2 - 11 }$

$( g \circ h )( 6 ) = \sqrt { 25 }$

$\large {\boxed {( g \circ h )( 6 ) = 5 } }$

To get a final output of 5 , she must first input 6 into machine h(x) , then the result from machine h(x) is input back to machine g(x).

Question b:

From the results above , it is possible to get a final output of -5.

It could be done by first input 6 into machine g(x) , then the result from machine g(x) is input back to machine h(x).

Learn more

Inverse of Function : brainly.com/question/9289171
Rate of Change : brainly.com/question/11919986
Graph of Function : brainly.com/question/7829758

Answer details

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: Function , Trigonometric , Linear , Quadratic

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