Answer:
C. f(x) = 1/3x + 5 and g(x) = 3x - 15
f^-1(21) = 5
Explanation:
To find the inverse. we exchange x and y and then solve for y
A. f(x) = 2x + 3 and g(x) = 0.5x - 3
y = 2x+3
x = 2y+3
x-3 = 2y
(x-3)/2 =y
This is not g(x)
B. f(x) = 1/6x - 2 and g(x) = 6x -12
y = 1/6 x -2
x = 1/6 y -2
x+2 = 1/6 y
6x +12 =y
This is not g(x)
C. f(x) = 1/3x + 5 and g(x) = 3x - 15
y = 1/3 x+5
x = 1/3 y +5
x-5 = 1/3 y
3x-15 =y
This is g(x) so it is the inverse
D. f(x) = x^2 +7 and g(x) = + or - squared x-7
y = x^2 +7
x = y^2 +7
x-7 = y^2
±sqrt(x-7) = y
This is not g(x)
3. f^-1 (21) = ?
f(x) = 2x+11
The functions are inverses so the input of 1 is the output of the other
f(a) = b means f^-1 (b) = a
We want to know when y =21
21 = 2x+11
Subtract 11 from each side
21-11 = 2x+11-1
10 = 2x
Divide by 2
10/2 = 2x/2
5 =x
f^-1(21) = 5