Answer: (a) -7 (b) [tex]\bold{\dfrac{4}{25}}[/tex] (c) [tex]\bold{-\dfrac{5}{2}}[/tex] (d) 4
Step-by-step explanation:
A) f(x) = 2x - 3 when x is between -5 and -2 (including -5 and -2)
B) f(x) = x² when x is between -2 and 2 (including 2)
C) [tex]f(x)=-\dfrac{3}{2}x+\dfrac{7}{2}[/tex] when x is between 2 and 5 (including 5)
a) Equation A includes x = -2
f(x) = 2x - 3
f(-2) = 2(-2) - 3
= -4 - 3
= -7
b) Equation B includes x = [tex]-\dfrac{2}{5}[/tex]
f(x) = x²
[tex]f\bigg(-\dfrac{2}{5}\bigg) = \bigg(-\dfrac{2}{5}\bigg)^2[/tex]
[tex]=\dfrac{4}{25}[/tex]
c) Equation C includes x = 4
[tex]f(x)=-\dfrac{3}{2}x+\dfrac{7}{2}[/tex]
[tex]f(4)=-\dfrac{3}{2}(4)+\dfrac{7}{2}[/tex]
[tex]=-\dfrac{12}{2}+\dfrac{7}{2}[/tex]
[tex]=-\dfrac{5}{2}[/tex]
d) Try each equation to see if x falls within the values given.
A) f(x) = 2x - 3
-2.5 = 2x - 3
0.5 = 2x
0.25 = x NOT VALID since x should be between -5 and -2
B) f(x) = x²
-2.5 = x²
[tex]\sqrt{-2.5}=x[/tex] NOT VALID since x cannot be an imaginary number
C) [tex]f(x)=-\dfrac{3}{2}x+\dfrac{7}{2}[/tex]
[tex]-\dfrac{5}{2}=-\dfrac{3}{2}x+\dfrac{7}{2}[/tex]
[tex]-\dfrac{12}{2}=-\dfrac{3}{2}x[/tex]
[tex]-\dfrac{12}{2}\bigg(\dfrac{2}{3}\bigg)=x[/tex]
[tex]4 = x[/tex] VALID since x is between 2 and 5
