which of the following about the function
f(x) = 2x, 0<x<1
1, x=1
-x+3, 1<x<2
is not true?
a. f(1) does not exist
b. limx->0+ f(x) exists
c. limx->2- f(x) exists
d. limx->1 f(x) exists
e. limx->1 f(x) ≠ f(1)
a. nope f(1)=1
b. true. it's 2
c. true. it's 1
d. true. it's 2
e. false -- see (a)
all these are easy to see if you graph f(x)
ok! thank you so much
To determine which of the following statements about the given function is not true, we can analyze each statement individually.
a. f(1) does not exist:
To check if this statement is true, we need to substitute x = 1 into the given function:
f(1) = 1
Since the function is defined as f(x) = 1 when x = 1, this statement is false.
b. limx->0+ f(x) exists:
To check if this statement is true, we need to evaluate the limit of the function as x approaches 0 from the right side.
limx->0+ f(x) = limx->0+ (2x) = 0
Since the limit exists and evaluates to 0, this statement is true.
c. limx->2- f(x) exists:
To check if this statement is true, we need to evaluate the limit of the function as x approaches 2 from the left side.
limx->2- f(x) = limx->2- (-x+3) = 1
Since the limit exists and evaluates to 1, this statement is true.
d. limx->1 f(x) exists:
To check if this statement is true, we need to evaluate the limit of the function as x approaches 1.
Since the function is defined as f(x) = 1 when x = 1, the limit as x approaches 1 of the given function is also 1.
Therefore, this statement is true.
e. limx->1 f(x) ≠ f(1):
To check if this statement is true, we need to evaluate the limit of the function as x approaches 1 and compare it to the value of f(1).
limx->1 f(x) = 1
f(1) = 1
Since the limit and f(1) both evaluate to 1, this statement is false.
Therefore, the statement that is not true is e. limx->1 f(x) ≠ f(1).