Which of the following pairs of functions are inverse functions?

Question

A)f(x)=3x-9, g(x)= -3x+9
B)f(x)=4-x, g(x)= 4+x
C)f(x)=x+5, g(x)= x-5
D)f(x)=x, g(x)= -x
explain

Answer 1

C is the only pair that is an inverse.
f(g(x)) = g(x) + 5
= x - 5 + 5 = x
g(f(x)) = f(x) - 5
= x + 5 - 5 = x
A, B and D are not inverses because
f(g(x)) does not equal x and g(f(x)) does not equal x.
In order for two functions to be inverses of each other, the following two things must be true.
1) f(g(x)) = x and
2) g(f(x)) = x
Note: Inverse of a function does NOT mean opposite.

Answer 2

c. f(x) = x + 5, g(x) = x - 5 Why? because substituting "x" for "f(x)" and "y" for "x".... f(x) = x + 5 ..... will develop into... x = y + 5 fixing for "y".... through including "-5" to each and every section... you get.... x = y + 5 -5 .... - 5 ------------- x - 5 = y + 0 x - 5 = y..... that may be written as y = x - 5.... which sounds like g(x) = x - 5 Tip: to locate if 2 applications are inverses of one yet another.... take between the equations and turn "x" to "y".... and "y" to "x"..... and be conscious in the experience that your ensuing equation resembles the second one equation..... you may want to ought to sparkling up for a variable to ascertain.... like I had to above....

Answer 3

c is an inverse because i dont know how to explain it. something about y=x and flipping the lines and iono