Can someone please check my answer fast?The function g is defined by g(x) = x+6 over/ 2x+5Find g(x+5)MY ANSWER : g+11 over/ 2x+15
Accepted Solution
A:
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! ________________________________________________________
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)"
________________________________________________________ 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" ;
→ 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! ________________________________________________________