Respuesta :
Your answer was: "g+11 over/ 2x+15 " .
____________________________________________________
Your answer was "incorrect —but almost correct" !
Instead of "(g + 11)" for the "numerator" ; you should have put: "(x + 11)" .
As a matter of technicality, you could have/should have stated:
________________________________________________________
{ [tex]x \neq - 7.5[/tex] } ; { [tex]x \neq -2.5[/tex] }.
________________________________________________________
→ {but this would depend on the context — and/or the requirements of the course/instructor.}. Good job!
________________________________________________________
Explanation:
________________________________________________________
Given: g(x) = [tex] \frac{(x+6)}{(2x + 5)} [/tex] ;
Find: g(x+5) .
To do so, we plug in "(x+5)" for all values of "x" in the equation; & solve:
________________________________________________________
Start with the "numerator": "(x + 6)" :
→ (x + 5 + 6) = x + 11 ;
__________________________________
Then, examine the "denominator" : "(2x + 5)"
→ 2(x+5) + 5 ;
→ 2(x + 5) = 2*x + 2*5 = 2x + 10 ;
→ 2(x+5) + 5 =
2x + 10 + 5 ;
= 2x + 15 ;
________________________________________________________
→ g(x + 5) = [tex] \frac{x+11}{2x +15} [/tex] .
________________________________________________________
Note that the "denominator" cannot equal "0" ;
since one cannot "divide by "0" ;
_______________________________________________________
So, given the denominator: "2x + 15" ;
→ at what value for "x" does the denominator, "2x + 15" , equal "0" ?
→ 2x + 15 = 0 ;
Subtract "15" from each side of the equation:
→ 2x + 15 - 15 = 0 - 15 ;
to get:
→ 2x = -15 ;
Divide EACH SIDE of the equation by "2" ;
To isolate "x" on one side of the equation; & to solve for "x" ;
→ 2x / 2 = -15 / 2 ;
to get:
→ x = - 7. 5 ;
Your answer was: "g+11 over/ 2x+15 " .
____________________________________________________
Your answer was "incorrect —but almost correct" !
Instead of "(g + 11)" for the "numerator" ; you should have put: "(x + 11)" .
As a matter of technicality, you could have/should have stated:
________________________________________________________
{ [tex]x \neq - 7.5[/tex] } ; { [tex]x \neq -2.5[/tex] }.
________________________________________________________
→ {but this would depend on the context — and/or the requirements of the course/instructor.}. Good job!
________________________________________________________
So; " [tex]x \neq - 7.5[/tex] " .
________________________________________________________
Now, examine the "denominator" from the original equation:
________________________________________________________
→ "(2x + 5)" ;
→ At what value for "x" does the 'denominator' equal "0" ?
→ 2x + 5 = 0 ;
Subtract "5" from each side of the equation:
→ 2x + 5 - 5 = 0 - 5 ;
to get:
→ 2x = -5 ;
Divide each side of the equation by "2" ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ 2x / 2 = -5 / 2 ;
→ x = -2.5 ;
→ So; " [tex]x \neq -2.5[/tex] " .
____________________________________________________
The correct answer is:
____________________________________________________
→ g(x + 5) = [tex] \frac{x+11}{2x +15} [/tex] ;
{ [tex]x \neq - 7.5[/tex] } ; { [tex]x \neq -2.5[/tex] }.
____________________________________________________
→ Your answer was: "g+11 over/ 2x+15 " .
____________________________________________________
Your answer was "incorrect —but almost correct" !
Instead of "(g + 11)" for the "numerator" ; you should have put: "(x + 11)" .
As a matter of technicality, you could have/should have stated:
________________________________________________________
{ [tex]x \neq - 7.5[/tex] } ; { [tex]x \neq -2.5[/tex] }.
________________________________________________________
→ {but this would depend on the context — and/or the requirements of the course/instructor.}. Good job!
________________________________________________________
____________________________________________________
Your answer was "incorrect —but almost correct" !
Instead of "(g + 11)" for the "numerator" ; you should have put: "(x + 11)" .
As a matter of technicality, you could have/should have stated:
________________________________________________________
{ [tex]x \neq - 7.5[/tex] } ; { [tex]x \neq -2.5[/tex] }.
________________________________________________________
→ {but this would depend on the context — and/or the requirements of the course/instructor.}. Good job!
________________________________________________________
Explanation:
________________________________________________________
Given: g(x) = [tex] \frac{(x+6)}{(2x + 5)} [/tex] ;
Find: g(x+5) .
To do so, we plug in "(x+5)" for all values of "x" in the equation; & solve:
________________________________________________________
Start with the "numerator": "(x + 6)" :
→ (x + 5 + 6) = x + 11 ;
__________________________________
Then, examine the "denominator" : "(2x + 5)"
→ 2(x+5) + 5 ;
→ 2(x + 5) = 2*x + 2*5 = 2x + 10 ;
→ 2(x+5) + 5 =
2x + 10 + 5 ;
= 2x + 15 ;
________________________________________________________
→ g(x + 5) = [tex] \frac{x+11}{2x +15} [/tex] .
________________________________________________________
Note that the "denominator" cannot equal "0" ;
since one cannot "divide by "0" ;
_______________________________________________________
So, given the denominator: "2x + 15" ;
→ at what value for "x" does the denominator, "2x + 15" , equal "0" ?
→ 2x + 15 = 0 ;
Subtract "15" from each side of the equation:
→ 2x + 15 - 15 = 0 - 15 ;
to get:
→ 2x = -15 ;
Divide EACH SIDE of the equation by "2" ;
To isolate "x" on one side of the equation; & to solve for "x" ;
→ 2x / 2 = -15 / 2 ;
to get:
→ x = - 7. 5 ;
Your answer was: "g+11 over/ 2x+15 " .
____________________________________________________
Your answer was "incorrect —but almost correct" !
Instead of "(g + 11)" for the "numerator" ; you should have put: "(x + 11)" .
As a matter of technicality, you could have/should have stated:
________________________________________________________
{ [tex]x \neq - 7.5[/tex] } ; { [tex]x \neq -2.5[/tex] }.
________________________________________________________
→ {but this would depend on the context — and/or the requirements of the course/instructor.}. Good job!
________________________________________________________
So; " [tex]x \neq - 7.5[/tex] " .
________________________________________________________
Now, examine the "denominator" from the original equation:
________________________________________________________
→ "(2x + 5)" ;
→ At what value for "x" does the 'denominator' equal "0" ?
→ 2x + 5 = 0 ;
Subtract "5" from each side of the equation:
→ 2x + 5 - 5 = 0 - 5 ;
to get:
→ 2x = -5 ;
Divide each side of the equation by "2" ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ 2x / 2 = -5 / 2 ;
→ x = -2.5 ;
→ So; " [tex]x \neq -2.5[/tex] " .
____________________________________________________
The correct answer is:
____________________________________________________
→ g(x + 5) = [tex] \frac{x+11}{2x +15} [/tex] ;
{ [tex]x \neq - 7.5[/tex] } ; { [tex]x \neq -2.5[/tex] }.
____________________________________________________
→ Your answer was: "g+11 over/ 2x+15 " .
____________________________________________________
Your answer was "incorrect —but almost correct" !
Instead of "(g + 11)" for the "numerator" ; you should have put: "(x + 11)" .
As a matter of technicality, you could have/should have stated:
________________________________________________________
{ [tex]x \neq - 7.5[/tex] } ; { [tex]x \neq -2.5[/tex] }.
________________________________________________________
→ {but this would depend on the context — and/or the requirements of the course/instructor.}. Good job!
________________________________________________________
