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In this lesson, we will learn how to add, subtract, multiply, or divide two given functions to create a new function and how to identify the domain of the new function.

Q1:

Determine the common domain of the functions π ( π₯ ) = β 7 π₯ β 7 1 and π ( π₯ ) = β 8 π₯ β 6 4 2 2 .

Q2:

If and are two real functions where and , determine the value of if possible.

Q3:

If π and π are two real functions where π ( π₯ ) = π₯ β 5 π₯ 2 and π ( π₯ ) = β π₯ + 1 , find the domain of the function ( π + π ) .

Q4:

If π βΆ ] β 7 , 8 ] β β 1 where π ( π₯ ) = π₯ β 2 1 , and π βΆ [ β 8 , 4 ] β β 2 where π ( π₯ ) = 4 π₯ + 8 π₯ + 3 2 2 , find ( π β π ) ( π₯ ) 2 1 and the domain of ( π β π ) 2 1 .

Q5:

If π βΆ β βΆ β + where π ( π₯ ) = π₯ β 1 7 , and π βΆ [ β 2 5 , 4 ] βΆ β where π ( π₯ ) = π₯ β 1 1 , then find ( π + π ) ( π₯ ) and its domain.

Q6:

If π β β β 1 β : where π ( π₯ ) = 4 π₯ + 4 1 , and π ] β 9 , 6 ] β β 2 : where π ( π₯ ) = π₯ β 1 2 , find and fully simplify ( π β π ) ( π₯ ) 1 2 and the domain of ( π β π ) 1 2 .

Q7:

Q8:

Q9:

Given that π βΆ β β β + , where π ( π₯ ) = π₯ β 1 9 , and π βΆ [ β 2 , 1 3 ] β β , where π ( π₯ ) = π₯ β 6 , evaluate ( π β π ) ( 7 ) .

Q10:

If π β β β 1 β : where π ( π₯ ) = β π₯ β 1 1 , and π ] β 9 , 1 [ β β 2 : where π ( π₯ ) = 5 π₯ β 3 2 , find ( π + π ) ( π₯ ) 1 2 and the domain of ( π + π ) 1 2 .

Q11:

If π and π are two real functions where π ( π₯ ) = π₯ β 5 π₯ 2 and π ( π₯ ) = β π₯ + 4 , determine the domain of the function ( π β π ) .

Q12:

Given that and find ο½ π π ο ( π₯ ) 2 1 and state its domain.

Q13:

Q14:

If π β β β : where π ( π₯ ) = 4 π₯ β 4 , and π [ β 8 , β 2 [ β β : where π ( π₯ ) = 5 π₯ + 5 , find the value of ( π + π ) ( 5 ) if possible.

Q15:

What is the domain of the quotient π π , in terms of the domains of π and π ? Assume that both domains are subsets of the set of real numbers.

Q16:

Given that and find ( π β π ) ( π₯ ) 1 2 and state its domain.

Q17:

If π and π are two real functions where and π ( π₯ ) = π₯ , find the domain of the function ( π β π ) .

Q18:

Q19:

Given that and find the value of ο½ π π ο ( β 1 ) if possible.

Q20:

Q21:

Given that , , and , determine in its simplest form.

Q22:

Given that π ( π₯ ) = 5 π₯ β 8 2 5 π₯ β 4 Γ· 2 5 π₯ β 3 0 π₯ β 1 6 1 2 5 π₯ + 8 1 2 2 3 , π ( π₯ ) = 2 5 π₯ β 4 5 0 π₯ β 2 0 π₯ + 8 2 2 2 , and π ( π₯ ) = π ( π₯ ) Γ π ( π₯ ) 1 2 , simplify the function π , and determine its domain.

Q23:

Given that π ( π₯ ) = π₯ β 3 6 4 π₯ β 1 Γ· 8 π₯ β 2 3 π₯ β 3 5 1 2 π₯ + 1 1 2 2 3 , π ( π₯ ) = 2 5 6 π₯ β 4 3 2 0 π₯ β 4 0 π₯ + 5 2 2 2 , and π ( π₯ ) = π ( π₯ ) Γ π ( π₯ ) 1 2 , simplify the function π , and determine its domain.

Q24:

If π ( π₯ ) = π₯ + 1 and π ( π₯ ) = π₯ + 1 2 , then find and fully simplify an expression for ( π β π ) ( π₯ ) .

Q25:

If π and π are two real functions where and π ( π₯ ) = 5 π₯ determine the domain of the function ο½ π π ο .

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