Pre-Calc 300
Inverse Functions & Linear Functions
Mr. Dooley
Name__________________________________
Inverse Functions: Two functions f and g are inverse functions if and only if  f g  ( x)   g f  ( x)  x .
1. Determine if the given functions are inverses of each other.
f ( x)  3x  2
g ( x) 
x2
3
2. Determine if the given functions are inverses of each other.
1
f ( x)  x  5
g ( x)  2 x  5
2
Steps For Determining An Inverse Equation
1) Replace f(x) with y
2) Switch the positions of x and y
3) Solve for your new y
4) Replace new y with f⁻¹(x)
3. Find the inverse of the function.
x6
f ( x) 
3
4. Given f ( x)  x  2 , find f 1 ( x) .
5. Given g ( x)  x 2  9 , find g 1 ( x).
Linear Functions:
Slope-intercept form: y  mx  b
Point-slope form:
y  y1  m  x  x1 
Ax  By  C
Standard form:
Parallel lines: Lines with equal slopes and different y-intercepts.
Perpendicular lines: Lines with opposite reciprocal slopes.
6. Find the equation of the line through (8, 7) and (18, 2) in:
a. Point-Slope Form
b. Slope-Intercept Form
c. Standard Form
d. Now find the parallel line in slope-intercept form that passes through the point (3, 9)
e. Now find the perpendicular line in slope-intercept form through the point (-4, 1)
HOMEWORK: page 17 #22-27 and page 26 #23-28 (use your graphing calculator)