Answer:
a) The function is equal to 0 when [tex]x = 0[/tex].
b) The function is equal to 30 when [tex]x = 3[/tex].
c) The function is equal to -12 when [tex]x = -3[/tex].
d) The function is equal to [tex]a\cdot (a+7)[/tex] when [tex]x = a[/tex].
e) The function is equal to [tex]x\cdot (x-7)[/tex] when [tex]x = -x[/tex].
Step-by-step explanation:
To this respect we must keep in mind that this exercise consists in evaluating given function at different values. Let [tex]f(x) = x^{2}+7\cdot x[/tex] the function to be evaluated:
a) [tex]x = 0[/tex]
[tex]f(0) = 0^{2}+7\cdot (0)[/tex]
[tex]f(0) = 0[/tex]
The function is equal to 0 when [tex]x = 0[/tex].
b) [tex]x = 3[/tex]
[tex]f(3) = 3^{2}+7\cdot (3)[/tex]
[tex]f(3) = 30[/tex]
The function is equal to 30 when [tex]x = 3[/tex].
c) [tex]x = -3[/tex]
[tex]f(-3) = (-3)^{2}+7\cdot (-3)[/tex]
[tex]f(-3) = -12[/tex]
The function is equal to -12 when [tex]x = -3[/tex].
d) [tex]x = a[/tex]
[tex]f(a) = a^{2}+7\cdot a[/tex]
[tex]f(a) = a\cdot (a+7)[/tex]
The function is equal to [tex]a\cdot (a+7)[/tex] when [tex]x = a[/tex].
e) [tex]x = -x[/tex]
[tex]f(-x) = (-x)^{2}+7\cdot (-x)[/tex]
[tex]f(-x) = x^{2} -7\cdot x[/tex]
[tex]f(-x) = x\cdot (x-7)[/tex]
The function is equal to [tex]x\cdot (x-7)[/tex] when [tex]x = -x[/tex].
