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If \(f(x) = 2x + 1\), then which of the following must be true?
A. \(f(0.5x−1) = x\)
B. \(f(x−0.5) = x\)
C. \(f(x−1) = x\)
D. \(f(0.5x−0.5) = x\)
E. \(f(−0.5x) = x\)
A. \(f(0.5x−1) = x\)
B. \(f(x−0.5) = x\)
C. \(f(x−1) = x\)
D. \(f(0.5x−0.5) = x\)
E. \(f(−0.5x) = x\)
09 May 2023, 02:06
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If f(x)=2x+1, then which of the following must be true?
For all the options less option D, the LHS is not equal to RHS.
Option D - f(0.5x - 0.5) = x
substitute 0.5x - 0.5 in given function, we get
LHS: f(0.5x-0.5) = 2(0.5x - 0.5) + 1= x - 1 + 1 = x = RHS
Answer D
For all the options less option D, the LHS is not equal to RHS.
Option D - f(0.5x - 0.5) = x
substitute 0.5x - 0.5 in given function, we get
LHS: f(0.5x-0.5) = 2(0.5x - 0.5) + 1= x - 1 + 1 = x = RHS
Answer D
26 Nov 2023, 08:10
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\(f(x) = 2x + 1\) , Let's take each option choice and solve for it.
A. f(0.5x−1) = x
To find f(0.5x−1) we need to compare what is inside the bracket in f(0.5x−1) and f(x)
=> We need to replace x with 0.5x−1 in f(x) = 2x + 1 to get the value of f(0.5x−1)
=> f(0.5x−1) = 2*(0.5x−1) + 1 = x - 2 + 1 = x - 1 ≠ x => FALSE
B. f(x−0.5) = x
=> f(x−0.5) = 2*(x−0.5) + 1 = 2x - 1 + 1 = 2x ≠ x => FALSE
C. f(x−1) = x
=> f(x−1) = 2*(x−1) + 1 = 2x - 2 + 1 = 2x - 1≠ x => FALSE
D. f(0.5x−0.5) = x
=> f(0.5x−0.5) = 2*(0.5x−0.5) + 1 = x - 1 + 1 = x => TRUE
We don't need to solve further but solving to complete the solution
E. f(−0.5x) = x
=> f(−0.5x) = 2*(−0.5x) + 1 = -x + 1 ≠ x => FALSE
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
A. f(0.5x−1) = x
To find f(0.5x−1) we need to compare what is inside the bracket in f(0.5x−1) and f(x)
=> We need to replace x with 0.5x−1 in f(x) = 2x + 1 to get the value of f(0.5x−1)
=> f(0.5x−1) = 2*(0.5x−1) + 1 = x - 2 + 1 = x - 1 ≠ x => FALSE
B. f(x−0.5) = x
=> f(x−0.5) = 2*(x−0.5) + 1 = 2x - 1 + 1 = 2x ≠ x => FALSE
C. f(x−1) = x
=> f(x−1) = 2*(x−1) + 1 = 2x - 2 + 1 = 2x - 1≠ x => FALSE
D. f(0.5x−0.5) = x
=> f(0.5x−0.5) = 2*(0.5x−0.5) + 1 = x - 1 + 1 = x => TRUE
We don't need to solve further but solving to complete the solution
E. f(−0.5x) = x
=> f(−0.5x) = 2*(−0.5x) + 1 = -x + 1 ≠ x => FALSE
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
