Answer:
a) f(-1/2) = -2 is NOT TRUE.
b) f(0) =3/2 is TRUE.
c) f(1) = -1 is NOT TRUE.
d) f(2) = 1 is NOT TRUE.
e) f(4) = 7/2 is TRUE.
Step-by-step explanation:
Here, the given function is [tex]f(x) = (\frac{1}{2}) x+\frac{3}{2}[/tex]
Now, checking for each values for the given function:
a) Putting x = (-1/2):
[tex]f(\frac{-1}{2} ) = (\frac{1}{2})(\frac{-1}{2} ) +\frac{3}{2} = \frac{-1}{4} + (\frac{3}{2} )\\\implies f(x) = \frac{-1 + 6}{4} = (\frac{5}{4} )[/tex]
and (5/4) ≠ -2
Hence, f(-1/2) = -2 is NOT TRUE.
b)Putting x = 0 :
[tex]f(0) = (\frac{1}{2})(0 ) +\frac{3}{2} = (\frac{3}{2} )[/tex]
Hence, f(0) =3/2 is TRUE.
c) Putting x = 1:
[tex]f(1 ) = (\frac{1}{2})(1 ) +\frac{3}{2} = \frac{1}{2} + (\frac{3}{2} )\\\implies f(x) = \frac{3 + 1}{2} = (\frac{4}{2} ) = 2\implies 2 \neq -1[/tex]
Hence, f(1) = -1 is NOT TRUE.
d)Putting x = 2:
[tex]f(2 ) = (\frac{1}{2})(2 ) +\frac{3}{2} = 1+ (\frac{3}{2} )\\\implies f(x) = \frac{2 + 3}{2} = (\frac{5}{2} )[/tex]
and (5/2) ≠ 1
Hence, f(2) = 1 is NOT TRUE.
e)Putting x = 4:
[tex]f(4 ) = (\frac{1}{2})(4 ) +\frac{3}{2} = 2 + (\frac{3}{2} )\\\implies f(x) = \frac{4 + 3}{2} = (\frac{7}{2} )[/tex]
Hence, f(4) = 7/2 is TRUE.
