The true statements for the given piecewise function are: (a) f(1) = 5 and (d) f(2) = 4.
The function which is defined by the pieces of different functions over different intervals is said to be a piecewise function.
The given piecewise function is
f(x) = 2x for x < 1; f(x) = 5 for x = 1; f(x) = x² for x > 1
(a) Calculating f(1):
Since x = 1 then f(x) = 5;
So, f(1) = 5
Hence this statement is true.
(b) Calculating f(5):
Here x = 5 i.e., x > 1 then f(x) = x²
So, f(5) = 5² = 25
Hence the given statement f(5) = 1 is false.
(c) Calculating f(-2):
Here x = -2 i.e., x < 1 then f(x) = 2x
So, f(-2) = 2(-2) = -4
Hence the given statement f(-2) = 4 is false.
(d) Calculating f(2):
Here x = 2 i.e., x > 1 then f(x) = x²
So, f(2) = 2² = 4
Hence the given statement f(2) = 4 is true.
Therefore, statements (a) and (d) are true.
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Question: Given the piecewise function shown below, select all the true statements. (you can choose more than one answer)
f(x) = 2x for x < 1; f(x) = 5 for x = 1; f(x) = x² for x > 1
(a) f(1) = 5
(b) f(5) = 1
(c) f(-2) = 4
(d) f(2) = 4
