For the function f(x) = 4x - 5 determine whether f(x) is one-to-one. If so, find
ID: 3031575 • Letter: F
Question
For the function f(x) = 4x - 5 determine whether f(x) is one-to-one. If so, find a formula for the inverse, give the domain and the range for f^-1, and then graph both functions on the same axes. Is f(x) a one-to-one function? Yes No The inverse function is f^-1 = Choose the correct domain below. [- infinity, infinity] (- infinity, 0) (0, - infinity) (- infinity, infinity) Choose the correct range below. (- infinity, infinity) [- infinity, infinity] (- infinity, 0) (0, - infinity) Choose the correct graph for f and f^-1 belowExplanation / Answer
a)
SInce f(x) is linear, it is increasing function
hence it is one to one function
b)
let
y = 4x-5
4x = (y+5)
x = (y+5)/4
= (1/4)*y + 5/4
so,
f-1(x) = (1/4)*x + 5/4
c)
f(x) = 4x-5
since x can take any values,
domain is (-infinity,infinity)
Answer D
d)
range is (-infinity,infinity)
Answer A
e)
Just plot both the graph
It matches A
Answer: A